The Jags boss is desperate to bolster his squad further this month after snapping up former Falkirk striker Lyle Taylor.
Archibald revealed he did consider making a move for the Hoops midfielder but now looks unlikely to follow up his initial interest.
He said: "He was one we looked at but I don't think Dylan is fit.
"We've not contacted Celtic or pursued that to be honest. We've not enquired about him.
"He was just a player we were aware of - a good player - but that was as far as it went."
However, talks are still ongoing with regards to extending Gary Fraser's loan period at Thistle.
The midfielder is back at Bolton following his spell in Glasgow and, despite serving a seven-match ban for violent conduct, Archibald wants to secure his return to Thistle.
He said: "We are keen to get him back.
"He's down having talks with Bolton so we will see what happens. I think they are thinking it over.
"We are low on numbers and losing players every week.
"We are definitely looking to get some players in but we are just finding it very difficult."
Archibald moved quickly to secure Taylor on loan from Sheffield United when the transfer window opened.
And he insists he was not disappointed to miss out on Brentford's Farid El Alagui - who has joined Dundee United on loan - because Taylor was his top choice.
Archibald said: "Lyle was our number one target even back when we won promotion.
"We had a board meeting and they asked me who I wanted and Lyle was the player we wanted then.
"He (El Alagui) was on our list but Lyle was top of the list so we are delighted with what we got."
Meanwhile, Isaac Osbourne is unlikely to play again this season after going under the knife to cure an ankle problem.
Archibald confirmed: "Osbourne had his operation today and I think that will be his season over."