The Germany international was a target for former Red Devils boss David Moyes and is well known to the Scot’s successor, Van Gaal.
Kroos previously worked under the Dutchman at the Allianz Arena for two years and has become a key member of Pep Guardiola’s side.
The 24-year-old was identified as a prime candidate to boss United’s midfield, with his contract at Bayern entering its final year.
However, reports have now suggested that Kroos will not be reunited with the current Netherlands coach at the Theatre of Dreams after the World Cup as Van Gaal has other irons in the fire.
Bayern president Karl Hopfner told Kroos they will not be increasing the contract offer currently on the table.
The Germany international’s deal at the Allianz Arena is set to expire in June, and negotiations with Bayern over new terms have stalled following heavy interest from Manchester United.
Bayern, though, are refusing to be bullied into upping their financial offer, with Hopfner telling Kicker: “There will certainly be further talks. But at some point the player has to say what he wants.
“We will not exceed certain financial boundaries.”
Hopfner moved to highlight the case of Michael Ballack, who left the club for Chelsea in 2006, as an example as to how Bayern will not be strong-armed into any action.
“It was the same with Michael Ballack and at some point we withdrew the offer,” the chief concluded.