Christensen's contract at Chelsea is due to expire at the end of June, while Kessie's AC Milan deal will also expire next week, and both players are said to have agreed switches to Camp Nou.
Barcelona are planning to overhaul their squad this summer, though, with a report claiming that head coach Xavi wants to bring eight new players to Camp Nou in the current market.
Here, Sports Mole picks out five players that the club could potentially sign on free transfers ahead of the 2022-23 campaign.
Barcelona are pushing to sign Lewandowski this summer, but it is a complicated deal, and a recent report claimed that Edinson Cavani has been identified as an alternative to the Poland international.
The 35-year-old had a disappointing 2021-22 campaign at Manchester United, only managing two goals and one assist in 20 appearances for the club in all competitions.
Cavani will leave the Red Devils with a record of 19 goals and seven assists in 59 appearances, though, and he will certainly believe that he can still perform at the top level.
The Uruguay international scored over 300 times during spells with Napoli and Paris Saint-Germain, and he is said to be keen to secure a move to La Liga this term despite interest from elsewhere.
Cavani was linked with a switch to Barcelona in January, and he could be a genuine option for the club if Lewandowski remains at Bayern beyond the end of the summer market.
Paulo Dybala is leaving Juventus on a free transfer this summer, and Inter Milan are believed to be at the head of the queue for the Argentina international.
However, Barcelona are also said to be admirers of the 28-year-old, and it would certainly not be a surprise to see him make the move to Camp Nou on a free transfer.
Dybala enjoyed a successful 2021-22 campaign for Juventus, scoring 15 goals and registering six assists in 39 appearances in all competitions.
The South American has struck 115 goals in 293 appearances for the Old Lady in total, meanwhile, in addition to registering 48 assists.
Dybala is not believed to be firmly on Barcelona's radar at this stage, but he could become a genuine option for the club if Ousmane Dembele leaves on a free transfer at the end of the month.
Angel Di Maria's contract at Paris Saint-Germain is expiring at the end of June, and the 34-year-old has been strongly linked with a switch to Juventus over the last few weeks.
However, a recent report claimed that Barcelona are also keeping a close eye on the situation, with the Catalan outfit ready to explore the possibility of bringing the Argentine to Camp Nou.
Di Maria was again a regular for PSG during the 2021-22 campaign, making 31 appearances in all competitions, contributing five goals and nine assists in the process.
The South American previously played in Spain for Real Madrid between 2010 and 2014, representing the club on 194 occasions in all competitions before making the move to Manchester United.
Juventus are said to have offered Di Maria a one-year deal with the option of a further 12 months, but he is waiting to see whether Barcelona make a move.
Andrea Belotti is set to become available on a free transfer at the end of June, having failed to come to an agreement over a new contract with Torino.
The 28-year-old scored eight times and registered one assist in 23 appearances in all competitions at club level during the 2021-22 campaign, while he has netted 113 goals and registered 28 assists in 251 appearances for the Bull since arriving from Palermo in 2015.
Belotti is certainly different to Barcelona's current options in the final third of the field, and a number of clubs are believed to be keeping a close eye on the Italian's situation.
The Catalan giants will continue to push for Lewandowski, but if a deal for the forward becomes impossible, then a move for Belotti on a free transfer certainly makes sense considering his impressive record.
Corentin Tolisso is preparing to leave Bayern when his contract expires at the end of June, and a number of clubs have been credited with an interest in the midfielder.
The 27-year-old only made 22 appearances for his German club last term due to injuries, but he has featured on 118 occasions for the Munich giants since arriving from Lyon in July 2017.
Tolisso recently insisted that he has the drive and desire to return to his best level, having found it difficult in recent years due to a number of fitness problems.
"I am convinced that [my issues] are more psychological than physical," he said recently. "It's more in my head than with my body. I worked with a mental coach to put words to what I was going through. Now, I'm 5,000% convinced I can get back to a very high level physically."
Frenkie de Jong's possible departure to Man United would open up a spot in the Barcelona squad, and although Kessie's signature has allegedly already been secured, central midfield is an area in need of bolstering ahead of the 2022-23 campaign.