Luque and his father Eugenio Botas, who is his agent, agreed the deal when they met with representatives from Newcastle in La Coruña on Thursday night.
Newcastle have offered Deportivo just over £9m for the 27-year-old, although the Galicians want at least £10m in order to recoup the money they paid for him.
Luque, who can play up front or on the left side of midfield, joined Deportivo from Mallorca in 2002 after scoring 14 goals with the islanders. He is a regular in the Spanish squad and has been linked with Barcelona, Real Madrid and Atletico Madrid.
Deportivo's new coach Joaquin Caparros is said to be prepared to let the player go in order to raise funds for a possible move for Argentina international Andres D'Alessandro. Graeme Souness' side have already made unsuccessful bids for both Michael Owen and Nicolas Anelka to fill the gap left by Craig Bellamy in attack.
Stuart Pearce, the Manchester City manager, insists Trevor Sinclair remains in his plans despite attempts to bring another right midfielder to the club.
Sinclair, who has spent the past year out with a knee injury, started last weekend's goalless draw against West Bromwich Albion in the right-wing role once occupied by Shaun Wright-Phillips.
Pearce, who wants Bolton's Stelios Giannakopoulos for that position, said: "Trevor has worked extremely hard to get back. The fact I am looking for a player in a similar position is not a slight on him in any way, I need to have competition in every position and hopefully if I do bring someone in it will spark Trevor that little bit more.
"He has done everything we've asked of him, he's playing in a more natural role on the right rather than the left-hand position he was in 18 months ago and with Shaun leaving he will get even more chances there."