Liverpool have heavily been linked with the Bayern Munich star, but appear to be waiting to see if the German club drop their asking price.
Bayern want around £27million for their midfielder, who saw his stock soar again during his side’s triumphant Champions League run last season.
United have been mentioned as potential rivals to Liverpool for Thiago’s signature and have reportedly held talks with the Spaniard’s representatives.
However, the Manchester Evening News claim United have no such interest and feel they are being used by Bayern and Thiago and his team to put pressure on Liverpool to finalise a move.
Thiago’s contract expires in less than 12 months and Bayern would much prefer to cash in on the 29-year-old now rather than lose him for nothing next summer.
The player himself is determined to link up with Jurgen Klopp at Liverpool after seven years at Bayern.
The transfer window will remain open until 5 October and Liverpool have made just one addition to their senior squad so far.
Kostas Tsimikas was signed from Olympiacos as cover at left-back, but there are rumours Klopp is keen to further strengthen the depth in his squad.
Liverpool opened their 2020/2021 Premier League campaign with a thrilling 4-3 victory over Leeds United at Anfield last weekend.
He said: ‘If I invented a word that would end speculation, I could become really rich. I can’t end speculation as long as the transfer window is open.
‘Thiago Alcantara is a really good player. It’s nice we are linked with him but that’s pretty much all really.
‘He’s a good player, Liverpool is a big club, so it’s nice, but apart from that, I’ve got nothing to say. Unfortunately I cannot end the speculation.’