The left full-back was offered a new contract two months ago but has made it clear that he will not be signing the proposal.
"They don't want to spend in the club and bring in quality players, that's why everybody [wants to] go," the former Villareal player said on Twitter.
"The club has allowed all the major players in the team to leave. Andy Carroll, Kevin Nolan, etc. Seriously, do you think this is the fault of the players?
"This club will never fight again to be among the top six with this policy.
"They tell lies all the time. They have not offered me more money."
Enrique is reportedly being targeted by Liverpool manager Kenny Dalglish.