Liverpool are frontrunners to complete a deal for Thiago this summer but they have not yet submitted a bid for the 29-year-old, who is valued at €30 million (£26.8m) by Bayern.
Messi, meanwhile, has told Barcelona that he wants to leave the club this summer and City are now working on a deal to add the Argentine to Pep Guardiola’s squad.
Rooney expects Liverpool and City to be battling for the Premier League title once again but the former Manchester United captain believes Jurgen Klopp’s side will have the edge if they complete a deal for Thiago.
Rooney also believes United and Chelsea are still a year away from competing with City and Liverpool for the title, even though Frank Lampard has Timo Werner, Hakim Ziyech and Ben Chilwell as new additions to his squad.
Asked for his title prediction in an interview with talkSPORT, Rooney replied: ‘I think it’s City or Liverpool.
‘Chelsea are making a lot of signings, some good signings.
‘Man United have a lot of potential in the players they have got but I still think they are a year away.
‘I think Chelsea with the new signings will possibly need a year to get everyone on the same song-sheet.
‘So I do think it is between City and Liverpool. And I think if Liverpool get Thiago from Bayern Munich, I think it [the title] is done.
‘I think that’s a better signing than Messi going to Man City.’