Bojan, 24, joined Stoke from Barcelona in the summer for £1.5 million and, after a somewhat slow start to life at the Britannia Stadium, has started to show elements of the talent which saw him once labelled “the next Messi”.
Notching four goals in the past 11 games from a withdrawn role, his recent resurgence has not gone unnoticed at Liverpool, with manager Brendan Rodgers said to have been more than impressed with his performances.
The Northern Irishman declared this week that things would be quiet on the transfer front at Anfield in the current window, but it's claimed he would be keen to bring the former La Masia product to the club if the chance presented itself.
Liverpool’s troubles up top have been well-documented this season, having seen Mario Balotelli, Fabio Borini and Rickie Lambert all struggle in front of goal with Daniel Sturridge out, while summer signing Divock Origi is not expected to cut his Lille loan short.
Sturridge is set to return at some stage in the coming weeks, and Raheem Sterling has thrived in a central role in recent games, but the Reds could still do with additional help to aid their Champions League push over the second half of the campaign.
Bojan has not been a prolific scorer during his time at Stoke, but his creativeness and Barca pedigree would still make him an appealing signing.
Having made his Nou Camp debut at 17, the one-time capped Spaniard would go on to score 41 goals in 162 games over the next four seasons for the Catalan giants, while winning three La Liga titles and two Champions League winner’s medals in the process.
His career would stagnate following disappointing spells in Serie A with Roma and AC Milan, as well as on loan at Ajax after returning to his childhood club, but if Rodgers could help him unlock his potential then he might just prove a shrewd signing.
However, having penned a contract until 2018 at Stoke, a sizeable fee would no doubt have to be involved.