The France international is wanted by Barcelona and United, though the Red Devils are ready to cool their interest should they prise Sanchez away from Arsenal.
However, City may not be ready to sign him at the end of the season.
Pep Guardiola is reportedly a huge admirer of Griezmann and, with Sanchez likely to move to Old Trafford, City may try to land the Frenchman instead.
And Don Balon say Barcelona are worried about missing out on the Atletico striker.
They think United’s transfer for Sanchez will damage their hopes of landing Griezmann in the summer.
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Alexis Sanchez to Man Utd: Barcelona fear Man City will try to sign Antoine Griezmann
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Mourinho says he is not unconfident of signing Sanchez
Yet whether Barcelona even have the finances to pull off a deal remains to be seen.
The Catalan giants have spent big on two players in the last few months after losing Neymar to PSG.
Ousmane Dembele was the first to arrive, signing from Borussia Dortmund for £120million in August.
And they then followed that up by snapping up Philippe Coutinho from Liverpool for £142m.