Iron boss Brian Laws is looking for backup to first choice forwards Billy Sharp and Andy Keogh after new signing Ramon Calliste was ruled out for six months with an ankle injury.
Ghana-born Asamoah fell out of favour with the Imps last season and finished the season on loan at Chester, where he netted eight times in 17 games.
A left-winger is still a target for Laws, who is hoping to bring in a player on loan from a Premiership club.