The Firhill gaffer has already added striker Lyle Taylor to his ranks after the former Falkirk forward signed a loan deal from League One side Sheffield United.
Lack of a cutting edge has cost Thistle dear in the Premiership so far this term. It means Archibald is eager to bolster his attack again before the end of the window to boost his side in the fight to avoid the play-offs this term.
And SportTimes understands McGeouch is on his list of targets after Lennon admitted he could allow the forward and his fellow-Parkhead kids to leave on loans.
McGeouch has struggled to make the breakthrough into the Hoops first team and could find his chances limited further if Lennon is successful in bringing in his own attacking transfer targets.
A temporary switch to Firhill would suit all parties, with Thistle monitoring the situation of the Scotland Under-21 international as the Jags scour the market.
Archibald has previously expressed an interest in Brentford striker Farid El Alagui, but SportTimes understands Motherwell's Bob McHugh is not one of his targets after speculation that he could be on his way to Firhill this month.
Meanwhile, midfielder Stuart Bannigan will miss the matches against Ross County and St Johnstone after being sent off against Hearts.