The Bulgaria international is currently playing for Levski Sofia in his homeland, but has a clause in his contract which allows him to leave the club on a free transfer.
He was left out of Sunday's game against Botev Plovdiv and reports have claimed that he is now discussing a move to West Ham.
Levski sporting director Georgi Ivanov told Bulgarian National Radio: "We had to let him go because we have an agreement. I allowed him to travel to England because I am contractually required to do so.
"But he remains a Levski player until he signs with another team."
West Ham manager Sam Allardyce is in the market for a new striker after losing Andy Carroll for around four months due to an ankle injury.
Bojinov previously spent three years at City after joining from Fiorentina in 2007, but his time at the Etihad Stadium was wrecked by knee and Achilles injuries.
The 28-year-old made just 12 appearances for City, with his only goal for the club coming against Tottenham Hotspur in 2009.
He has subsequently played for the likes of Parma, Sporting Lisbon and Vicenza before linking up with Levski earlier this year.