The 24-year-old stand-off, a former South Africa under-20 international, was a solid threat for the Warriors in their 36-33 friendly triumph over Ulster at Scotstoun on Saturday.
With Adam Hastings and Pete Horne away with Scotland at the World Cup, it looks likely that Thomson will get a decent run in the No 10 jersey in the opening part of the Guinness Pro14 season.
Glasgow start their league campaign away to the Cheetahs on 27 September and Rennie said: “Brandon is a good player. In terms of our attacking play he did well against Ulster and he is learning all the time as he gets more and more game time at this level.
“He had a good season for us last year and he is becoming more vocal out there on the pitch and I am looking forward to seeing how he goes in the early part of the season.
“They are a good side, Ulster, so it was a real arm wrestle and could have gone either way, but it was nice to get the win.”
Rob Herring and Rob Lyttle both scored tries early on as Ulster went 12-0 up before a good Warriors spell put them 17-12 up at half-time.
A penalty try was followed up by an effort by Rory Hughes and then Brandon Thomson kicked a penalty to put them ahead.
Stuart McCloskey scored Ulster’s third try just after half-time before Johnny Matthews went over for Glasgow.
A penalty try for Ulster preceded Glenn Bryce’s converted score to put the home side up 31-26 with 19 minutes to go.
James Hume’s converted try six minutes later again put the men from Belfast ahead before the winning try came from replacement prop Adam Nicol for Glasgow.