Archibald was on Swindon Town's managerial shortlist last season and has been linked with other vacancies.
Osman says the loss of Archibald - who guided Thistle to a top six finish last season - would be a hard act to follow.
"Since I signed, he's only got better, every season. It's no surprise teams are interested in him," Osman said.
"We don't want him to go anywhere. He's probably one of the best managers I have played under.
The boys love him. We just pray he stays here for another season."
Osman's Partick Thistle team-mate Adam Barton echoes his captain's sentiments.
"I would be personally disappointed because what he has done is really good," the midfielder said.
"As a footballer, you like managers who really stick by their players. You come across so many managers who chop and change things and I have been through that many managers that many times.
"New managers come in and they don't even want to see you play, they just want to bring their own players in and chop and change. To see him go would not be a good thing."
Partick Thistle are on the verge of losing promising centre-back Liam Lindsay, who has travelled to Barnsley for a medical following the clubs agreeing a fee for the player.
Subject to the completion of the medical, Lindsay will sign a three-year deal at Oakwell.
Partick Thistle captain Abdul Osman says the players are praying manager Alan Archibald stays at the club for another season.