Spanish midfielder Thiago has been heavily linked with a move to Anfield both before and after helping Bayern Munich to a sixth Champions League triumph during the season-ending mini-tournament in Lisbon.
However, it remains to be seen if a deal for the 29-year-old - who has less than 12 months left to run on his current contract in Bavaria - can be struck, with the Premier League champions having previously made it clear they would not be splashing the cash this summer following the coronavirus pandemic.
So far Liverpool have made only one addition to the squad that sealed a first domestic league title for three decades in 2019-20, with Greek left-back Kostas Tsimikas signed from Olympiacos in an £11.75million deal to provide competition for Andy Robertson.
Meanwhile, Standard Sport understands that the Reds' title rivals Manchester City believe they are Messi's favoured next destination after the six-time Ballon d'Or winner officially informed Barcelona of his desire to leave Camp Nou this summer after 20 years.
Pep Guardiola previously coached the Argentine with great success in Catalonia, while the latter is believed to maintain a good relationship with City chief executive Ferran Soriano.
Most would surely laud Messi to the Etihad as the greatest signing in Premier League history were it to come to fruition, though former Manchester United and England captain Rooney believes Thiago to Liverpool would be a better deal and guarantee a second successive title for Jurgen Klopp's dominant side.
“I think it is City or Liverpool [for the title],” the Derby County skipper told talkSPORT on Thursday.
“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.
“Chelsea with the new signings will possibly need a year to get everyone on the same songsheet.
“So I do think it is between City and Liverpool. And if Liverpool get Thiago from Bayern Munich, I think it is done [the title].
“That is a better signing than Messi going to Man City.”