The 19-year-old only joined the German club during last year's summer transfer window, signing from Swedish outfit Malmo for a fee of £7.6m.
Since arriving in the Bundesliga, Larsson has quickly established himself as an important first-team player, featuring 17 times in the league so far.
Although primarily being a defensively-minded player, the midfielder has shown his ability to contribute at the top end of the pitch, finding the net against German champions Bayern Munich on December 9.
According to German outlet Bild, Liverpool are hoping to beat Premier League rivals Arsenal to the signature of Larsson at some stage in 2024.
The report claims that a switch away from Frankfurt during the current window is improbable, with a transfer more likely to occur at the conclusion of the campaign.
Dino Toppmoller's men are said to be in no rush to offload the Swedish starlet, who is contracted at the club until the summer of 2028 after signing from Malmo just over six months ago.
It has been claimed that Frankfurt would demand a fee of £68.2m for Larsson in the summer window, with the midfielder drawing comparisons to Manchester City duo Kevin de Bruyne and Rodri since arriving in the Bundesliga.
Liverpool are supposedly set to continue their midfield rebuild in 2024 after the likes of Alexis Mac Allister, Ryan Gravenberch and Wataru Endo moved to Anfield in the summer.
Jurgen Klopp's engine room was the primary focus for improvement ahead of the current term, following the departures of long-serving players such as Jordan Henderson and James Milner.
Arsenal are also said to be interested in recruiting Larsson this year, with the Gunners looking to add further quality to their midfield after the acquisitions of Kai Havertz and Declan Rice before the 2023-24 term.
After splashing over £200m on new signings in the summer, Mikel Arteta's side have been deadly silent in terms of incomings during the January window as they aim to stay on the right side of FFP rules.
The North Londoners have let three players leave on the final day of the window so far, with Charles Sagoe Jr, Runar Alex Runarsson and Bradley Ibrahim departing on a mixture of loan and permanent deals.
With Liverpool and Arsenal highly unlikely to secure Larsson before Thursday night's deadline, the four-time Sweden international will play a part when Frankfurt travel to FC Koln in the Bundesliga on Saturday.