New interim Scotland head coach Scott Johnson has reportedly decided to go with the Glasgow fly-half at No.10, paired with Edinburgh skipper Greig Laidlaw, who will be play at scrum-half.
The 24-year-old is one of 19 Warriors named in Johnson's training squad which will gather at Scotstoun for three days next week.
Although John Barclay, Chris Cusiter and Jon Welsh are all still officially classed as injured, they have also been invited to attend.
Jackson said: "I know certain things have been said in the papers, but until I see the team-sheet and my name is on it I will take nothing for granted.
"The first target was to make the Scotland training squad and then the second will be to make the match-day 23 and hopefully the team.
"If that's the way things work out it would be fantastic and to play in tandem with Greig would be great.
"First, though, I need to show I am operating at the top of my game against Northampton for Glasgow and then in the Scotland squad at Scotstoun next week.
"I know the competition at 10 will be intense with Tom Heathcote and Duncan Weir. I will just keep my head down, work as hard as I can and hopefully I can figure."
Meanwhile, Troy Nathan is to leave Warriors following Saturday's Heneiken Cup clash against Northampton Saints on Saturday.
With Nathan's regular position in the centre becoming an extremely competitive spot this season the two parties have agreed his release from the club.
He said: "I'm sorry to be leaving before the end of the season. I've enjoyed my time in Glasgow and I wish the Warriors squad all the best with the current campaign.
"I haven't found another club yet, but I've never been fitter and I'm optimistic about the future."