Alonso has made it clear to Reds boss Rafa Benitez that he is looking for a future in La Liga now after five years at Anfield.
It is understood however that Benitez is very reluctant to part company with Alonso, who he signed from Real Sociedad for Â£10.4million in 2004.
The Reds look ready to accept no less than Â£35million for Alonso, who has three years left on his current deal on Merseyside.
Today’s Echo says:
The 27-year-old is due to join up with his Liverpool team mates on Sunday after being given extended leave following his involvement in the Confederations Cup in South Africa but Alonso and his agent Inaki Ibanez are hopeful that a deal can be thrashed out with Real before then.
Meanwhile report this morning suggest that Benitez will do all he can to keep Argentine international midfielder Javier Mascherano at the club after speculation linking him with a big money move to Barcelona.
It is thought Liverpool will offer Mascherano a new and improved contract in a bid to keep him at the club. Some reports earlier in the summer have suggested Mascherano has felt left behind by recent contract renewals and improvements at the club.
The Daily Mail reports:
He is unsettled as his wife does not want to return from Argentina and Barcelona have expressed strong interest. But Liverpool will look to nearly treble his pay to keep him.
Liverpool have also completed the signing of 18-year-old French defender Chris Mavinga from Paris St Germain and Damien Plessis has been linked with a loan move to Cardiff City.