But after Atletico were banned from registering new players until 2018, Griezmann made the decision to stay and signed a new five-year deal worth £235,000-a-week.
But Luis claims the ex-Real Sociedad star was always happy with the La Liga giants and only spoke about United to secure himself the best possible contract.
‘[Griezmann] is a kid who speaks very clearly,’ Luis told El Mundo.
‘Often players talk when they feel they are not being valued as they deserve. Then they get more attention. He would have had many offers from many teams.
‘A player of his size wants to be up with the biggest in terms of contract and value. And that is fair – as Griezmann is doing great here.
‘In the end, for all the talk about other clubs, he always wanted to stay here and he is still here, happy and liking it.’
Griezmann is understood to have kept his £88million release clause in his contract, opening the door to the possibility of a move to United next summer.
However, Luis is hopeful that the 26-year-old will remain with Atletico for years to come after putting the transfer speculation behind him.
‘For sure, he can stay much longer,’ the former Chelsea defender added.
‘We hope the fans understand this and everything gets back to normal, although he has been scoring goals, and goals cure everything.’