The 25-year-old, who has won 42 caps for his country, has been linked with moves to a number of leading European clubs over the past few seasons, including Premiership heavyweights Liverpool, Chelsea and Manchester United.
"I have achieved everything that is possible at Betis," he said in Spanish daily As.
"I have told (Betis coach Javier) Irureta that it is time for me to leave for another club."
The midfielder, who is contracted to Betis until the summer of 2010, said he had been the subject of a 15million euros (Ã‚Â£10.2m) bid from Valencia, who are willing to include Uruguayan winger Mario Regueiro as part of the deal.
Joaquin was a member of Spain's last two World Cup squads.
Should United make an approach to Betis to sign him, your thoughts please.