The Betfair odds on Declan Rice signing for Bayern Munich this summer were cut from 25/1 to 15/2 amid speculation that Thomas Tuchel may try to bring the England midfielder to the German champions.
Arsenal had been fancied to sign Rice from West Ham, and the Gunners remain 4/6 favourites, but the 24-year-old will have plenty of suitors.
Manchester United have long been linked and they are 11/2 to add Rice to their midfield.
But the price movement on Bayern indicates that they could make a surprise bid.
The Germans have underperformed since Tuchel took over in March, and look set to miss out on the Bundesliga title for the first time in 11 seasons on Saturday.
Ex-Chelsea boss Tuchel is expected to get the funds for a squad rebuild this summer, however, and a defensive midfielder will be high on his list of priorities.
Rice is one of the most coveted in that position and, with West Ham playing Fiorentina in the Europa Conference League final on 7 June, he has the chance to end his Hammers career on a high.