The 32-year-old midfielder has spent the last 14 years with Los Che, having joined the club as a promising teenager in 1995.
He has gone on to make over 300 appearances for the club, picking up two league titles and a UEFA Cup success along the way.
Angulo has also won 11 caps for Spain and turned out for his country at the 2000 Olympics in Sydney.
He has, however, slipped down the pecking order at the Mestalla and is keen to revive his career elsewhere.
His agent, Jose Luis Tamargo, believes an agreement will be reached and he expects Angulo to be released from his contract in the next few days,
"He has been in Valencia for many years and I believe this solution is favourable for everyone," he said.
Angulo is reported to have already opened talks with Bolton regarding a move to England, with a contract awaiting him at the Reebok Stadium.
However, Blackburn are also believed to be keen, while Tenerife would offer the experienced playmaker the opportunity to remain in his homeland.