The Gunners need a miracle to end the season in fourth position, but will qualify for the 2019-20 Champions League if they beat Chelsea in the Europa League final on May 29.
Eleven wins, seven draws and 19 defeats - that is how Burnley have performed in the Premier League this season. A total of 40 points has left them in 15th position in the table - nine clear of 18th-placed Cardiff City.
The highest that Burnley can finish this season is 14th, but that would rely on the Clarets beating Arsenal and seeing Newcastle United lose at already-relegated Fulham.
Having finished seventh in the Premier League last season, it is difficult to brand the campaign a success for Sean Dyche's side. There was a period earlier in the campaign where relegation looked a real possibility, though, and securing another season of top-flight football must be seen as a positive.
Three straight wins between March 30 and April 13 effectively secured their survival, while they also picked up an impressive point at Chelsea towards the end of last month.
Burnley have actually scored 44 league goals this season, which is a club-record in the top flight. They have conceded 65, though, which is 26 more than in the entirety of the 2017-18 campaign. It has been a very different season for Dyche's side, but as mentioned, they have been able to starve off the threat of relegation.
It will not come as a surprise to learn that the Clarets have taken more points at home (23) than on their travels (17) this season. Nine defeats have arrived in front of their own fans, though, and a loss this weekend would bring an unwanted record in terms of home defeats in a single campaign.
Burnley have also lost nine successive meetings with Arsenal in all competitions, but the hosts will certainly be the fresher of the two teams this weekend, and will fancy their chances of ending their 2018-19 campaign with a positive result ahead of what is an important summer transfer window.
Recent form: WWWDLL
Arsenal sit fifth in the Premier League table ahead of the final set of fixtures. It is still possible - mathematically at least - for the Gunners to take fourth, but that would rely on a lot of things falling their way.
Indeed, to claim fourth spot, Unai Emery's side would have to beat Burnley, hope that Tottenham Hotspur lose at home to Everton, and also see an eight-goal swing in goal difference. It is not impossible, but it is very difficult to see the club securing a spot in next season's Champions League via their league position.
The Gunners will have another chance to qualify for next season's premier European competition, though, as they face Chelsea in the final of the Europa League later this month. Indeed, an impressive 4-2 win in Valencia on Thursday night saw them advance to Baku, where their London rivals will be waiting.
Arsenal have actually only won one of their last six matches in all competitions, while they have lost three of their last four in the Premier League. A home loss against Crystal Palace on April 21 was followed by defeats at Wolverhampton Wanderers and Leicester City, before being held at home by Brighton & Hove Albion last weekend.
The Gunners have the third-best home record in the top flight this term, but have suffered eight losses on their travels, claiming just six wins in the process. Addressing the team's form on the road will be imperative if Emery is to lead a title charge during his time at the club.
The fact that the London outfit have kept just two clean sheets in their last 28 top-flight away matches suggests that they will need to score at least twice in order to pick up all three points this weekend. That said, the 13-time English champions have won 1-0 in the last three league encounters at Turf Moor.
Not too many of Arsenal's defenders have covered themselves in glory this season, but Pierre-Emerick Aubameyang continued his excellent season with a hat-trick against Valencia on Thursday night. The Gabon international now has 29 goals for the campaign, including 20 in the Premier League.
In the grand scheme of things, the clash with Chelsea in Baku is far more important than this match, but Arsenal could finish sixth once again if they lose against Burnley, with fifth-placed Manchester United big favourites to collect all three points at home to Cardiff on the same afternoon.
Recent form: LWLLLD
Recent form (all competitions): LLLWDW
There will also be a spot for Dwight McNeil, who has impressed many with his performances this term. The 19-year-old has managed three goals and five assists in the Premier League during the 2018-19 campaign and the Clarets will do well to keep him this summer.
Burnley possible starting lineup:
Heaton; Lowton, Tarkowski, Mee, Taylor; Gudmundsson, Westwood, Cork, McNeil; Barnes, Wood
Arsenal possible starting lineup:
Leno; Lichtsteiner, Sokratis, Mustafi, Monreal; Guendouzi, Xhaka; Mkhitaryan, Ozil, Iwobi; Aubameyang
Head To Head
As mentioned, Arsenal have won each of the last nine meetings between the two teams in all competitions, including a 3-1 success in the reverse game at the Emirates Stadium earlier this season.
Not since December 2008 have Burnley beaten the Gunners, and that was in the League Cup.
September 1974 was the last time that the Clarets overcame Arsenal in the league, which is an indication of the size of the task facing the home side on Sunday afternoon.
We say: Burnley 1-1 Arsenal
Burnley will certainly be the fresher of the two teams having not played since last Friday. Arsenal's excellent record against the Clarets cannot be ignored, though, and we fancy a low-scoring draw.