The Russian Football Union (RFU) stressed Fabio Capello remains under contract with the national team.
Shakhtar Donetsk claim there has been no approach from Liverpool for in-demand midfielder Henrikh Mkhitaryan.
The 21-year-old striker has struggled to break into Blues' first team and will now get a chance to prove his worth in Turkey's top flight, signing a three-and-a-half-year deal.
Elazigspor are currently 16th in the 18-team Super Lig.
Wolverhampton-born Jervis moved to Blues from Shrewsbury at the age of 15 and graduated through the club's Academy, making a handful of substitute senior appearances without finding the net.
He enjoyed loan spells with Hereford, Notts County, Swindon, Preston, Carlisle, Tranmere and Portsmouth - the latter three coming over the first half of this season.
Jervis' contract at St Andrew's was due to expire in the summer.
Blues manager Lee Clark told the club's official website: "We wish Jake all the best and he's got himself a great opportunity playing in the Turkish top flight."