The Danish publication claims the two clubs are leading the race for the 23-year-old’s signature, but there are also six other teams interested in the player.
The Danish international is not expected to be available on the cheap, though, with Frankfurt initially placing a €30m (£26m) to €35m (£30m) valuation on the player.
However, Ekstra Bladet claim that, due to the competition for Lindstrom, that figure could rise to as much as €55m (£47m) if multiple clubs do make bids.
Lindstrom can play in multiple positions
While the Dane did play most of his games as a no.10 for Frankfurt last campaign, he has also been deployed as a winger on both flanks, as well as a striker.
Earlier in his career, Lindstrom was also deployed in deeper-lying midfield positions, although his strengths do lie in the final third of the pitch.
Last season, he bagged 9 goals and contributed 4 assists in 38 appearances for Frankfurt.
Klopp wants Liverpool to sign midfielders
Before the 4-0 friendly win over Leicester City at the weekend, manager Jurgen Klopp made it very clear that he wants to strengthen the midfield:
“We know we have to do something there, that’s absolutely clear. We are working on solutions, but I think everybody can imagine that.”
Lindstrom could be a target as the Reds seek a replacement for captain Jordan Henderson. Their reported pursuit of Southampton’s Romeo Lavia, meanwhile, may well be anticipating the imminent departure of Fabinho, whose move to Al-Ittihad is expected to be confirmed very soon.