Arsenal are building towards their Premier League opener away to Brentford on August 13, while Chelsea will begin their 2021-22 campaign at home to Crystal Palace on August 14.
Arsenal opened their preparations for the new campaign with a 2-1 defeat at Scottish side Hibernian on July 13 before drawing 2-2 with Rangers in their second friendly of the summer four days later.
The Gunners have since put back-to-back wins on the board, though, thumping Millwall 4-1 last weekend before beating Watford by the same scoreline at their training centre on Wednesday night.
Eddie Nketiah, Alexandre Lacazette, Kieran Tierney and Miguel Azeez all found the back of the net for the North London club, who will now take on Chelsea and Tottenham Hotspur in their final two pre-season fixtures.
Mikel Arteta's side, who announced the signing of Ben White on Friday afternoon, will begin their 2021-22 Premier League campaign away to newly-promoted Brentford on August 13 before taking on Chelsea and Manchester City in their next two league fixtures.
In addition to White, the Gunners have signed Albert Sambi Lokonga and Nuno Tavares this summer, and the club are still believed to be working on deals for at least two more players before the transfer deadline.
Chelsea, meanwhile, will take on Arsenal and Tottenham in their final two friendlies of the summer before facing Villarreal in the UEFA Super Cup at Windsor Park on August 11.
The Blues will then open their 2021-22 Premier League campaign at home to Palace on August 14, and it will be fascinating to see what transfer business has occurred at Stamford Bridge ahead of that contest.
Marcus Bettinelli has arrived on a free transfer, but the club have thus far been frustrated in their pursuit of a new centre-forward, with deals for Borussia Dortmund's Erling Braut Haaland and Bayern Munich's Robert Lewandowski all but ruled out, which has seemingly left Inter Milan's Romelu Lukaku as their leading target.
Thomas Tuchel's side opened their preparations for the new campaign with a 6-1 victory over Peterborough United in a behind-closed-doors friendly, with Hakim Ziyech netting a hat-trick for the European champions.
Chelsea will enter this match off the back of a 2-1 win over Bournemouth on Tuesday night, with Armando Broja and Ike Ugbo on the scoresheet for the Premier League club, who are now preparing for back-to-back fixtures against two London rivals in quick succession.
Arsenal boss Arteta is expected to make changes to the side that started against Watford on Wednesday, with Emile Smith Rowe, Thomas Partey, Lacazette and Rob Holding among those potentially coming into the side.
Lokonga could earn another spot in the middle of the park, but White is unlikely to be involved for the Gunners this weekend, having only completed a move to the Emirates Stadium on Friday afternoon.
There could be a debut for Bettinelli between the sticks, but the side will have a similar look to the one that featured against Bournemouth last time out.
Tammy Abraham continues to be linked with a number of clubs, including Arsenal, but the Englishman could be in the starting XI for Chelsea at the Emirates Stadium on Sunday afternoon.
Arsenal possible starting lineup:
Leno; Cedric, Holding, Mari, Tierney; Lokonga, Thomas; Pepe, Smith Rowe, Aubameyang; Lacazette
Chelsea possible starting lineup:
Mendy; Sterling, Miazga, Sarr; Zappacosta, Drinkwater, Loftus-Cheek, Alonso; Ziyech, Abraham, Pulisic
We say: Arsenal 1-1 Chelsea
Neither manager will be too worried about the result this weekend, but neither will want to lose this close to the start of the new Premier League season. The amount of changes that will occur throughout the contest is likely to harm the flow, and we are expecting the two teams to play out a low-scoring draw this weekend.
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