Kroos, out of contract at the end of next season, is angling for a new deal at the Allianz Arena but his wage demands are "through the roof", according to Bayern president Franz Beckenbauer.
United manager David Moyes has watched Kroos twice this year, most recently at Arsenal, where the Germany midfielder produced a virtuoso performance and hit the winning goal in Bayern's last 16 Champions League win.
Moyes was also pictured speaking with Kroos' agent during Bayern's win at Borussia Mönchengladbach in January, and now the 24-year-old's brother has admitted he could move to Manchester.
"We've already talked about (Toni's potential move to Manchester United)," Werder Bremen star Felix Kroos told Sky Germany.
"Manchester has been my dream team since I was a child. But I don’t give him any advice.
"He will take a good decision all by himself. There are worse situations than having to decide something like that."
Moyes is believed to have earmarked Kroos and İlkay Gündoğan, the Borussia Dortmund No.8, as his primary midfield targets this summer.
Despite concerns over his future at Bayern, Kroos played the whole 90 minutes of their 5-1 evisceration of Schalke on Saturday.