The Sun says American owners Fenway Sports Group want to see the squad numbers trimmed.
And in Meireles they have a man who would command a hefty fee.
The Reds would want at least a small profit on their original outlay - to help fund Dalglish's rebuilding with the Kop chief focusing on domestic buys.
Ironically Meireles was handed the shirt vacated by Alberto Aquilani at Anfield after the Italian had been loaned to Juve for the season.
But the Serie A club insist they have no plans to make his move permanent. However, they are expressing a major interest in Meireles.
Inter Milan are also in the hunt.