Reports from the UK indicate the clubs are set to hold talks over the deal in the next 48 hours, after Swansea originally rejected a £10m-plus-player deal for the 22-year-old.
The player had a release clause in his contract allowing him to speak to certain clubs if they offered £15m, and following the earlier rejection Liverpool have reportedly increased their offer to trigger talks.
Allen returned to training in Wales yesterday, but could find himself reunited with his former manager Brendan Rodgers, despite the new Liverpool coach having an agreement in his contract not to sign any Swansea players for the next 12 months.
Marseille midfielder Alou Diarra is set for a return to the English Premier League after moving closer to signing for newly promoted West Ham, according to reports in France.
The 31-year-old, who moved to the Stade Velodrome from Bordeaux last year, will join Sam Allardyce's side subject to a medical
Diarra, who has played for Lens and Lyon in Ligue 1, has already got experience of England's top flight, having spent a short time at Liverpool in 2002.
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The Israel international watched the club's friendly victory over Blackpool earlier this week, and looks set to join subject to a work permit.
The 25-year-old Colombian international has moved to the San Siro on a season-long loan, with an option to make the deal permanent.
Milan coach Massimillano Allegri said the deal would be one of the last the club made during the transfer window.
Villarreal have, meanwhile, signed Swedish international veteran Olof Mellberg from Olympiakos as a replacement for Zapata.
Martin O'Neill, the Sunderland manager, has already had a £10m bid for the 25-year-old rejected, and followed that up with an improved £12m bid this week.
However, the English championship side said they would not be rushed into cashing in on the player, whom Sunderland have identified as a replacement for Al Ain's Asamoah Gyan.
"Wolves can confirm that Steven Fletcher has handed in an official transfer request," the club said in a statement.
"The player's frustration stems from the fact that several bids have been rejected for his services, none of which meets the club's valuation.
"As previously stated, no player will leave Wolves unless the club's valuation is met."
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Hoffenheim have signed highly rated Spanish striker Joselu from Real Madrid for an undisclosed fee.
The 22-year-old forward - whose full name is Jose Luis Mato Sanmartin - had attracted substantial interest from across Europe after scoring 26 goals in 36 games for Real's B side, along with grabbing two goals in two appearances for the senior side.
He joins Hoffenheim - who finished 11th in the Bundesliga last season - on a four year deal.