Granada have a particularly strong interest in Garcia, 23, who spent last season on loan at Mouscron in Belgium.
For the first time ever, Granada qualified for the Europa League last season after finishing seventh.
Head coach Diego Martínez is looking for low-cost players of quality to ready his squad for their extra responsibilities.
Garcia has experience in La Liga and is a profile that appeals to several clubs in his homeland.
The interest in Garcia is not exclusively from Spain, with suitors elsewhere in Europe for the former Spanish under-21 international.
Galatasaray are another side looking for talented players on the cheap and have Garcia on a shortlist.
The Turkish club would offer Garcia a three-year contract, but are first assessing other options in the market.
Greece is also a possibility for Garcia, with AEK Athens keen on the technically gifted midfielder.
Garcia was a hot prospect at Man City after arriving from Villarreal in 2015. He made nine first team appearances before spending two seasons on loan at Girona.
Last season at Mouscron, he scored five goals and delivered three assists in 25 appearances.
With leagues now kicking off around Europe, Garcia hopes to resolve his future soon.