The German playmaker has been heavily linked with a switch to Old Trafford in recent months, with the club thought to have made him a top target.
But reports in recent times have suggested that United have backed off, which has opened the door for the Blues.
Jose Mourinho is believed to be keen to inject some more creativity into his side’s attack, and looks to have lost a little faith in Brazilian youngster Oscar, whose performances dipped over the latter half of the 2013/14 campaign.
Kroos is set to enter the final 12 months of his contract at Bayern, meaning that he will be free to walk away at the end of next season should an extension not be agreed.
The 24-year-old wants £150,000-per-week wages to be on a par with some of the Bundesliga champions’ top stars but the club are unwilling to match such demands.
Bayern are unlikely to let their man walk, and will instead sell for around £25m should a fresh contract not be agreed with the playmaker.