The 24-year old has been linked with a move to West Ham United - as reported by the Independent - and a return to Sunderland - by the Chronicle Live - where he enjoyed a successful loan spell two years ago.
But former Everton boss David Moyes has now formalised his interest in the player, with TMW reporting that the Spanish side have ‘initiated contact with the relevant parties’.
The Italian made just 15 appearances for the Reds last season - of which only four were starts – and managed just one goal in the process.
Sunderland had been his home the previous year, but their efforts to make his season-long loan a permanent deal last summer were thwarted by the player himself, after the two clubs agreed a fee - as covered by the Daily Mail.
Borini's destination this summer remains unclear but one thing which isn't in any doubt is that the former Chelsea youth star no longer features in Brendan Rodgers plans and it is now seemingly a case of when, not if, he leaves Anfield.