Liverpool have had a £10m bid for England right-back Nathaniel Clyne rejected by Southampton.
Clyne, 24, has become a target for the Reds with full-back Glen Johnson, 30, at the end of his Anfield contract.
They are expected to return with an improved offer for the former Crystal Palace player, who has one year left on his contract at St Mary's.
Liverpool are also pursuing Burnley striker Danny Ings and Manchester City midfielder James Milner.
The Anfield club are attempting to rebuild following a disappointing season under manager Brendan Rodgers, in which they finished sixth in the Premier league - two points above Southampton in seventh place - and failed to win a trophy.
Clyne joined the Saints from Palace in July 2012 and is under contract until the summer of 2016.
Liverpool took Adam Lallana, Dejan Lovren and Rickie Lambert from Southampton last summer for a combined total of almost £50m.
Before Gutierrez's departure was formally announced, he urged Ashley to consider what must be done to move the club forward after a last major trophy win in 1969.
Asked what needs to happen at Newcastle this summer, he told the Shields Gazette: “That’s a good question for the owner.
“I think the club has to learn what has happened in the last few years when they have been in charge of the club.
“It’s important to think about good and bad decisions. It’s good for learning, and to improve. They have to take note about what has happened during the last few years.
“They have to think what they are going to do, if they are going to go forward. They have to think about what is best for the city.”
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