The Premier League champions were heavily linked with the German international last month, but despite rumours of a £25m offer being readied, a transfer was not agreed.
United have since been linked with a fresh move for Kroos at the end of the season, with David Moyes still keen to add him to his under-performing squad.
But, the Scot will have to see off competition from the likes of Liverpool, Arsenal and Chelsea.
The three clubs have been alerted by Pep Guardiola’s admission that the 24-year-old may be allowed to move on and the player’s current contract stand-off with the Bundesliga champions.
The playmaker is believed to be looking to secure a massive wage rise to take his £60,000-per-week earnings to closer to the £150,000 mark to be on a par with some of the club’s other star names.
With 18 months left on his deal a summer sale may make sense for Bayern, even though his value will be decreased.
Manchester City are also said to be keen, which could see a scramble between the Premier League’s ‘big boys’ for Kroos after the World Cup.