The 23-year-old put in a solid display in Sunday's vital 13-8 victory at Treviso and will be hoping to get the nod for their final fixture with Connacht on May 5.
The crunch clash at Firhill could see Glasgow secure their second play-off berth in three years, and after playing his own part Dunbar has put his emergence all down to Lineen.
"Sean has given me loads of encouragement and worked very hard on rounding my game off," Dunbar told the Evening Times.
"As a former Grand Slam-winning centre he knows the position so well and how to get the best out of me.
"It has been great to get the run of starts in there because competition for places is so strong.
"Now we have one more game left against Connacht and hopefully I have done enough to stay in for that one because the atmosphere at Firhill will be incredible.
"We have given ourselves a great platform into the Connacht game with the win at Treviso and it is vital we make the most of that."
If Glasgow do secure fourth and third-placed Munster defeat Ulster then Lineen's side will face a tough trip to RaboDirect PRO12 leaders and European champions Leinster.
But Lineen is refusing to look any further ahead than next Saturday's visit of Connacht and insists Glasgow will need to be at their best to win.
"Connacht will make it incredibly tough for us to get the result we need, so it would be great to have another big Warriors crowd behind us as we push on for the win," said Lineen.
"Firhill has been a good home for us and we'll be doing everything we can to give the fans one last terrific memory to take away from the place."
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