Manchester United manager Jose Mourinho has questioned the mentality of some of his players, calling for them to break out of their "comfort zone".
If Mourinho can land his top two targets then United are likely to be a real force next season, especially when you already have the likes of Paul Pogba and Zlatan Ibrahimovic at the club.
Along with Griezmann, the Golden Boot winner as top scorer from UEFA Euro 2016, Mourinho will also renew a deal for Benfica defender Victor Lindelof, according to the Daily Mail.
Atletico Madrid's Antoine Griezmann kicks a penalty.
"In nearly every team the striker is the top scorer, I think so, unless you have another player with a special feeling to score goals coming from another position or you have another player scoring six seven or eight goals from penalties that is normal to happen".
Jose Mourinho has indicated that Manchester United won't be chasing impossible targets in the summer transfer window. We needed more time to play. "I am different in everything, I watch my team play in a hotel, I was forbidden to go to the stadium".
De Gea has been the Manchester United goalkeeper for every league match so far this season, so it would be shocking if he is not in the starting lineup against Leicester.
United are unbeaten in 14 Premier League games but have drawn their past three and been sixth in the table after each round of matches since 6 November.
The transfer window opens in the summer, and until the summer I think I have nothing to tell you. I am sure with training we will improve.
Looking ahead to facing champions Leicester City away in their next match on Sunday, Mourinho said: "It was incredible what Leicester did but I don't think it could be possible to do it in the second season with Champions League at the same time". I think I know what we need.
The Spanish club's president Enrique Cerezo last month revealed that United were pursuing the striker, while manager Diego Simeone has said that he will not hold back the team's prized asset.