The Brazil-born Spanish international left Atletico and made a switch to Chelsea in 2014. He helped the Blues win the title in his debut season and has impressed under Antonio Conte, scoring 14 goals in the league as the west London club sit comfortably on top of the table.
Griezmann has been linked with a move to Old Trafford as Jose Mourinho has made signing the France international his number one target. According to the Independent, United are expected to make a world-record bid of £100m ($123.4m) in securing the services of the Atletico star.
The La Liga outfit are set to use the funds from Griezmann's sale in re-signing Costa from Chelsea. They believe a bid of £40m ($49.3m) can help them secure their former player's signature.
However, the price tag could rise if Barcelona make their interest concrete in signing the Chelsea striker. The Catalan club could make Costa their main target to replace Luis Suarez at Camp Nou.
Both Atletico and Barcelona need to move quickly if they hope to sign Costa as there is interest from China for the Premier League's joint top scorer. Chinese Super League side Tianjin Quanjian owner Shu Yuhui has revealed the Blues are willing to part ways with their star player in the summer.
Yuhui admitted they are unlikely to wait until the end of the Premier League season before signing Costa. At the same time, Chelsea are unwilling to let their star player leave in January. Should the Premier League leaders retain Costa beyond the mid-season window, then Atletico and Barcelona could fight for his signature.
Costa's return to Atletico can allow United to land Griezmann in the summer as the Portuguese Mourinho will be looking to strengthen his squad before the start of the next season.