The Bundesliga giants view Rice as ‘the perfect defensive midfielder’ for the club and ex-Chelsea boss Thomas Tuchel is believed to be a huge fan of the player.
They made the 24-year-old England international a top transfer target and earlier this month the German club felt they were ‘close’ to securing his signature.
But Arsenal are still thought to be the favourites to sign Rice from West Ham and are believed to be preparing a £90m opening offer.
Like Bayern, Arsenal made Rice their top summer transfer target and like Tuchel, Mikel Arteta is also believed to be a ‘huge fan’, having already made plans regarding where he would fit in his system at the Emirates.
According to reports, Bayern have now identified Morocco international Amrabat as an alterative option if they miss out on Rice.
The 26-year-old Fiorentina star is wanted by both United and Barcelona this summer and would be a cheaper signing than Rice.
Amrabat has been playing in various top European divisions for the best part of a decade and shot to prominence after starring in Morocco’s impressive run to the World Cup semi-finals in Qatar.
He was linked with Chelsea and Liverpool during the January transfer window but ended up staying at Fiorentina, who just lost the Europa Conference League final to West Ham.
Amrabat recently spoke about his future and said: ‘Of course, the Premier League is a fantastic league, one of the strongest in the world. It would be nice to play there one day, but it’s not that I want only to go to England, because Spain is nice, Serie A is a nice league.’
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