With Isaac Osbourne and Sean Welsh both sidelined through injury, the Jags gaffer is eager to bolster his ranks before the end of the window on Friday night.
Defender Muirhead has stepped forward to play in the holding role in recent weeks and wants to retain his place in the long run.
Muirhead said: "At the back, you can get a breather sometimes.
"In the middle of the park, that doesn't happen so I'm trying to work on my fitness.
"It's different but it's not as big a problem if you make a mistake - there are always boys there to cover you.
"The gaffer is looking for midfielders but I believe I'm good enough to be in the team. If it means I have to challenge new players, then I'll do that.
"Maybe I could save the gaffer a bit of cash but Welshy will be back soon and he's a huge player for us."
Thistle host Dundee United this weekend as they aim to climb out of the SPFL Premiership relegation zone.
And forward Kallum Higginbotham could make a speedy return to action after suffering a cut on his knee in Saturday's draw at St Mirren.
Muirhead said: "Kallum trained today and hopefully he'll be okay for the weekend.
"He's one of our more attack-minded players and is always looking to create.
"We don't want to lose him for the Dundee United game, especially as Chris Erksine can't play.
"We all thought he'd miss a few games but he's the type who you can't keep away from training. Hopefully he's fit."
Muirhead added: "It was a disgusting injury. I didn't go over and see it at the time.
"Lee Mair turned to me and said, 'stay away'. He was nearly sick.
"I stayed away because I'm not one for blood. It was a nasty injury and hopefully he is okay for the weekend."
Meanwhile, Partick Thistle manager Archibald was an unused substitute as the Firhill Under-20 side beat Inverness Caley Thistle 4-2 yesterday afternoon.