The sale of Alonso would allow Rafael Benitez funds to sign Gareth Barry, although it is now believed that the England midfielder's transfer will be given the green light by Liverpool's owners.
Arsenal are keen to sign Alonso, but are reluctant to pay much more than the £!0.5 million Liverpool paid Real Sociedad for him four years ago.
"The value of Alonso in the market will be really high," admitted Benitez. "We are really pleased with him and we don't want him to go unless we get a very good price."
