The Mirror's John Cross claims the two sides have asked about taking Aspas on loan.
The 26-year-old arrived from Celta Vigo for a reported £7 million fee but has struggled with life at Liverpool so far, suffering from injury, struggling to adapt to the physical nature of the Premier League, and the form of Luis Suarez and Daniel Sturridge.
After starting the two matches against Hull City and Oldham in quick succession, it was back to the bench for Aspas at Stoke on Sunday, and with the return of Daniel Sturridge it looks increasingly less likely he'll be forcing his way into the starting XI any time soon.
Brendan Rodgers now has Suarez, Sturridge, in-form Raheem Sterling and Philippe Coutinho contesting the three forward positions in his side; Aspas is very much on the periphery.
The FA Cup tie at Bournemouth should provide an opportunity for Aspas, but aside from that, he looks like having an equally limited amount of playing time in the second half of the season as he has had thus far.
Aspas has certainly struggled to adapt to the Premier League, especially when used in a central role and lacking a physical presence of any sort.
More than anything though, Aspas strikes me as a player who needs regular football to be anywhere near his best—something he was obviously getting at Celta Vigo and hence how he attracted the interest of Liverpool.
But regular football is something he is not going to get any time soon at Anfield, even more so if Rodgers' pursuit of Mohamad Salah is successful.
He scored his first competitive goal for the club in the FA Cup tie against Oldham, but is unable to build on that momentum, something he clearly needs.
A move away from Anfield to a side who can offer him a starting place would certainly benefit Aspas, whether that be a loan deal or permanent.
The problem is though, Liverpool can't really afford to allow Aspas to leave until they sign a replacement for him. An injury to either of Suarez or Sturridge would leave Rodgers with only one first-team forward and Aspas, as mentioned, should be used in Cup ties to allow the key duo some rest.
The January transfer window so far has been very quiet but the two attacking players most heavily linked with Liverpool are Salah and Burnley's prolific young forward Danny Ings.
Burnley are unlikely to want to sell their key forward midway through the season and the 21-year-old's price—£8 million according to The Daily Mail—could prove a problem for Liverpool, who are looking for smart, financially sensible signings.
Likewise, the price of Salah could prove the stumbling block. The Daily Mail claim the Egyptian is valued at £16 million by Basle but Liverpool are looking to pay little over half that.
A year ago, Liverpool made two extremely savvy signings with Daniel Sturridge and Philippe Coutinho arriving for a a combined price of £20 million, but finding such bargains now is seemingly proving much trickier.
Of the two, Salah would be more likely to have an immediate impact, providing strength in depth in wide areas, while Ings would replace Aspas as the Reds' third-choice striker behind Suarez and Sturridge.
Aspas' replacement needs to be a young player who is relatively happy to learn from the lethal duo and can take any chances he gets in the first team.
For Aspas, he's at an age where he should be performing at his peak, especially having enjoyed one of his best seasons last year for Celta Vigo.
A move would certainly be wise for all parties, but Rodgers is right not to allow it until a replacement is signed.