Manchester United have submitted a €100m (£70m) bid for the Bayern Munich forward Thomas Müller, according to reports in Germany.

As reported by the Guardian on Monday, the 25-year-old, who played under the United manager Louis van Gaal at the start of his career, is open to leaving Bayern given his uneasy relationship with the coach Pep Guardiola. Now the German newspaper Bild has claimed that a bid – which would eclipse the world record amount for a player paid in euros – has been submitted by United, although Bayern are reluctant to sell.

However, the paper goes on to state that Müller is interested in leaving the Allianz Arena having completed 90 minutes in just 29 matches over the last two years since the arrival of Guardiola, despite the denial of his agent Ludwig Kögl: “I do not want to participate. Thomas plays for Bayern and has a contract with Bayern.”

Last week, the chairman Karl-Heinz Rummenigge promised that no other Bayern players would be following Bastian Schweinsteiger to Old Trafford. “I can totally reassure all the fans we will issue no further players more towards Manchester United,” he said.

“The Bundesliga has to finally act. The English are overtaking us left, right and centre. When taking into account transfer market activity, in marketing terms, in TV money – anywhere, really,” he said.

“The Bundesliga has to be careful not to fall further behind, I think. Anyone who follows the transfer market at the moment, within which English clubs work, knows their clubs are being fully upgraded. The Bundesliga has to be careful that we’re not emptied out.”

Cristiano Ronaldo’s move from United to Real Madrid in 2009 remains the costliest transfer fee in euros at €94m, €3m more than Gareth Bale’s move to the Santiago Bernabéu in 2013.