Rakitic has been linked with a move away from Barcelona for a while now and Juventus winger Costa could hold the key.
There are now a host of midfielders in the Barcelona squad and it's thought the Croatian is concerned for his long-term future.
The midfielder has made 21 appearances in the league this season, mainly as a substitute.
Despite Rakitic's plight, it's believed that he would prefer to stay in Spain, where his family are settled.
However, according to TV3 (via Forbes), Italian giants Juventus could be where Rakitic ends up.
The proposed switch that would see Costa head the other way has only become a reality since Rakitic's form improved.
The 32-year-old midfielder could be traded in for the 29-year-old Brazilian, who has struggled to cement his place in Juve's starting eleven.
This is mainly due to a string of injuries and the resulting inconsistency in form compared to those playing more regularly.
The Old Lady are believed to be open to letting Costa leave the club considering his unreliability.
Although, the Serie A leaders may face late competition for Rakitic from league rivals Inter Milan.
Barcelona are keen to make sure they get something useful in return for Rakitic, whose contract expires in 2021.
The Nerazzurri are keen to take the Croatian as part of a deal for Barcelona's high-priority target Lautaro Martinez.
The Argentinian striker is seen as the ideal long-term replacement for 33-year-old Luis Suarez.
Inter are also keen on La Blaugrana's Chilean midfielder Arturo Vidal - with coach Antonio Conte said to be a huge fan.
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