According to the Daily Express, Louis van Gaal is ready to rescue the Switzerland international from the Allianz Arena with a £18m offer for the midfielder when the transfer window reopens in six weeks time.
The 23-year-old attacker has been on the fringes of the first-team since his move from Basel and he slammed the German giants earlier this campaign for failing to give him an opportunity to impress.
Both van Gaal and Rodgers are keen on the playmaker, with Rodgers in particular thought to be lining up an offer for Shaqiri. Liverpool were believed to be interested in bringing Shaqiri to Anfield over the summer but the Swiss star stayed put as Pep Guardiola did not want to lose him.
But the Bundesliga side have now decided to grant Shaqiri's wish to move on for first-team football - but only if an interested club submits an offer of £18m or more.
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Manchester United are reportedly ready to agree to that asking price, as Louis van Gaal continues his overhaul of the Old Trafford club's squad.
Shaqiri would be another attacking midfielder for the Dutchman to add to his growing collection, with Adnan Januzaj, Angel Di Maria and Juan Mata already competing for a limited number of places alongside Wayne Rooney.
As for Liverpool, the Anfield club are weighing up whether to match United's offer. Rodgers wants to add to his squad following Liverpool's disappointing start to the season, but like United, attacking midfielder is not an area in need of urgent improvement.
Anfield attacking struggles
Adam Lallana and Lazar Markovic are still adapting to their new surroundings, so Rodgers is not sure adding another playmaker to them mix would be the right move.
Most important for Liverpool is getting Daniel Sturridge fit and healthy, and ready to partner the struggling Mario Balotelli in attack. The Italian is yet to score a Premier League goal for the Reds since his move back to England.