He pulled out of City's 3-2 pre-season friendly win at Stamford on Tuesday because he has yet to agree terms on a new deal. He was also left out of the team that lost 3-1 to Arnold Town on Thursday night.
Although insisting he wants to extend his stay with the club, he opted out of the games in case an injury scuppered his chances of finding a new club - should his contract talks with Lincoln end in a unsatifactionary manner.
Lincoln's Director of Football John Deehan insists the club are keen to retain the services of Birch after he scored 10 goals last term.
The stumbling block appears to be over Walsall-based Birch's request for the Imps to help finance midweek accommodation to cut down on his travelling time to training. Birch doesn't want to leave his Walsall home because his partner is expecting their first child. His travelling partners have recently left the Imps, leaving him alone to drive the journey every day.
Birch told the Lincolnshire Echo "I would like to have been offered a two-year contract to have a bit more security, but I would accept Lincoln's offer of a one-year deal - as long as everything felt right.
All I am asking for is a couple of nights accommodation in the week, so I don't have to keep travelling from the Midlands. My agent is currently in contact with a couple of Football League clubs and two in the Conference"
One of the Conference clubs is rumoured to be Tamworth.