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France international midfielder Nasri, 28, is set for at least another two months on the sidelines following a hamstring injury and tendon surgery in November.
The Colombia international, who has not played since October following a thigh injury, has been replaced in the squad by new loan signing Alexandre Pato.
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The next two points could help Chelsea in their hunt for Falcao as Monaco’s owner Dmitry Rybolovlev has a very stron relationship with fellow Russian billionaire and Blues owner Roman Abramovich.
Another factor that could bring Falcao to Stamford Bridge is the fact that his agent, Jorge Mendes, is also Jose Mourinho’s agent.
Falcao, who was linked with a deadline day move to former club Atletico Madrid, has been named in Chelsea's 25-man Premier League squad.
However, the Brazil international has not featured since November as he looks to regain full fitness following a series of injuries.
Neither spell was a success, with Falcao scoring four goals in 29 appearances for United and once in 12 for Chelsea.
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The Colombian spent the 2014-15 season on loan at Manchester United and then joined Chelsea last term.
The 29-year old has made just one Premier League start since signing on a season-long from Monaco last July.
The Gunners are expected to make one change, with new midfield signing Mohamed Elneny, 23, replacing defender Mathieu Debuchy, 30, who has joined Ligue 1 side Bordeaux on loan until the end of the season.
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The United States defender, 20, joined Chelsea on a four-and-a-half-year contract from New York Red Bulls last week.
Manchester City manager Manuel Pellegrini revealed on Monday that Nigerian forward Kelechi Iheanacho, 19, will replace Samir Nasri in City's 25-man Champions League squad.
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"June 24 will initiate training with @asmonaco," Falcao wrote on Instagram. "Excited and committed to start the pre-season with the club."
Since making his massive move from Atletico Madrid, Falcao has been watched and scouted by Mourinho’s team and reports in France are suggesting that they may make a formal bid in January, instead of holding off until the Summer.
The two European giants are desperate to land the Columbian after he has worked his way up to being one of the best strikers in world football, but both clubs will know that he won’t come cheaply.
Now a lot of people would imagine that Monaco are not going to listen to any offers for their star-man, but there are three important factors in this deal that could help.
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However, there are also reports suggesting that Cristiano Ronalo has made a plea to Madrid president Florentino Perez to sign the 27-year-old.
Former AC Milan forward Pato, 26, signed for Chelsea last week on a six-month loan from Corinthians.
Premier League outfit Chelsea are ready to step-up their interest in AS Monaco striker Radamel Falcao, but they will face some serious competition from Jose Mourinho’s old-side Real Madrid.
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He did not make Colombia's Copa America squad and now intends to restart his career with Monaco, where he has two years remaining on his contract.
Clubs featuring in the knock-out stages of the Champions League were required to supply European football's governing body Uefa with their updated squad lists by Tuesday night, but Arsenal have yet to publicly announce any changes to their 25-man squad.
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First of all, the French side are willing to listen to offers due to the UEFA Financial Fair Play rule which will be coming into action soon, so they may try and get high-earners off their wage-bill.
Chelsea interim boss Guus Hiddink has also included new signing Matt Miazga in both his Champions League and Premier League squad lists for the second half of the season.
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