"I had a chat with the City chairman Steve Lansdown and there is no deal on the table for Akinfenwa," Bateson told the official Torquay United website.
"Bristol City are neither prepared to make a cash payment nor are they willing risk a tribunal decision.
"He (Lansdown) did offer a deal that would have relied on Akinfenwa's success at the club, relating to his performances, etc., but I was not willing to go down this route."
League One new boys Swansea City are also said to be keen on signing Akinfenwa.