Manchester United wanted Griezmann this summer, with the France international becoming their No1 transfer target in the wake of their Europa League triumph in May.
However, after Atletico were banned from signing players until January, the Red Devils instead opted to splurge £75million on Everton hitman Romelu Lukaku.
Chelsea are set to finally offload Costa after Atletico agreed a £53million transfer fee with Antonio Conte’s side.
And the Daily Mail say the signing of the Chelsea centre-forward will boost Manchester United’s hopes of landing Griezmann further down the line.
The signing of Costa represents a significant buy for numerous reasons.
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Firstly, Atletico are managing to secure the return of a player who was liked by manager Diego Simeone and adored by their fanbase.
And they are also signing a striker that has won his team three league titles in the last four years.
Atletico are also blessed to be playing in their brand new stadium, the Wanda Metropolitano.
The Daily Mail say Simeone is likely to make Costa and Griezmann the focal points of his attack after the move goes through in January.
However, United will have a greater chance of signing the latter at the end of the season.
Whether or not he is needed, however, remains to be seen.
Lukaku has settled in magnificently, scoring seven goals in his first seven appearances for his new employers.
And, with Marcus Rashford and Anthony Martial thriving and Zlatan Ibrahimovic yet to come, Jose Mourinho may have a tough decision to make at the end of the season.