Matthews moved to Scotland in 2017 to play for Boroughmuir in the Premiership. Two good seasons at club level and Scotland Club XV honours - as well as a training stint with Edinburgh Rugby - put Liverpool-born Matthews in the mix and he has been with Glasgow since 2019.
His opportunities so far have been from the bench so he's eager to make the most of his opportunity against the men from Ulster.
"I'm looking to string a few games together while the boys are away and make the best of that opportunity," the 27-year-old, who is battling for the number two jersey with Grant Stewart (if released from Scotland bubble) and Fijian Mesu Dolokoto currently
"I think I've come on a lot working under first Dave Rennie and now Danny Wilson. My game fitness, game play and game understanding have all developed, and now in the next few games, I want to prove I should be in that matchday 23 more regularly.
"Boroughmuir is a great club, but I knew that if I wanted to kick on and become as good a player as my potential will allow me to, then I had to move up to this level and give myself a chance.
"Getting asked to train with Edinburgh for cover after my first few months at Boroughmuir made it a realistic goal for me to try to stick around for as long as possible in Scotland and try and make it as a pro.
"I was frustrated last week with the call-off [against Benetton], the whole squad was to be fair. We had prepared really well ahead of it, but you can't do much about the Scottish weather.
"We're a tight-knit group here at Glasgow with a good culture that has always been prominent. The boys stay close and together and train well.
"The players and the coaches have been really good at keeping the group together [during a disrupted season]. We're just looking to get all of the next few games on the fixture list played. We're going to push to make the Champions Cup again [for 2021/22] so thatís our aim as a group.
"We're very confident we can do that. We've got a couple of really big games coming up [Ulster and Leinster] and Ospreys have still got to come here as well which will be a great opportunity to claw back some points."