The Scotland duo have both been out of action - Peter with a broken hand and Tommy with a back problem.
Kenny Murray has revealed both have been running with the team this week, so far without any sign of a problem.
Glasgow's assistant coach told The Herald: "Pete [Horne] has been training – trained well. If he gets through and comes out without any problems he will be in the mix for this weekend. Tommy [Seymour] trained well too. Hopefully he will be in the mix as well."
The real excitement at the club, though, has been giving the players their first look at Brian Alainu'uese, the Simona U20s lock they have signed on a short-term contract from Waikato in New Zealand to cover the sudden crisis in the second row.
"I can tell you, he is a big man," said Kenny. "I watched him doing some tackling, there is a lot of momentum behind that body. I will be really excited to see him on the pitch.
"He arrived last Saturday, trained Monday and yesterday and did not look out of place. There is a lot to learn in a short period. If we are comfortable with where he needs be with plays and set piece plays then he will also come into consideration for this week.
"We have had a few X-factor players over the years - guys like Niko [Matawalu] and Leone [Nakaraswa] - and with his size in particular he could be a potential X-factor player. He is a really nice guy as well, a nice humble, quiet person but I imagine that might change on the pitch."