West Ham are resigned to losing Rice in the next summer transfer window due to interest from some of the biggest clubs in the Premier League.
Arsenal have been laying down groundwork on trying to sign Rice for several months and he is their top target for the next transfer window.
Manchester United and Liverpool are also interested but Bayern Munich are now getting serious about getting their hands on Rice as well.
According to German broadcaster Sky Deutschland, Thomas Tuchel and the Bayern Munich hierarchy have identified him as one of their top targets.
With the prospect of Bayern Munich not winning the league this weekend, the club want to make a big splash in the transfer market this summer.
Rice is a player they want and they are now considering paying the big money required to sign the midfielder.
There were suggestions that Bayern Munich might not get into a bidding war for a player who is priced at £100m by West Ham.
But the midfielder is now a top target and the German champions are now ready to compete with the English clubs for him.