The Scotland U21 and A international has helped the Warriors reach the heights of the fourth and final play-off place after ten rounds of this season's RaboDirect PRO12.
Scottish rivals Edinburgh have found the going far tougher and sit ninth in the table ahead of their bid to reclaim the historic trophy over two games starting at Murrayfield on Boxing Day.
But with Gunners wing Tim Visser's eight scores putting him top of the try table and a recent draw against the struggling Dragons still fresh in his mind, Grant is taking nothing for granted.
"These are massive games, if you look at the league table we're pushing for a play-off spot and there are eight valuable points there for us to take," he said.
"Not only that there is also the 1872 Cup at stake which we won last year and we want to hold onto this year.
"Our run speaks for itself in the RaboDirect Pro 12 and if we're going to be there at play-off times then these are two games that we need to take points from.
"Our ultimate goal is to get to that play-off spot, to get in the top four and to do that we need to continue winning whether that is against Edinburgh or anyone else.
"I always keep one eye on Edinburgh and they've been playing some good rugby recently and they've got Tim Visser out on the wing who is scoring a lot of tries for them at the minute.
"We've got players that match them in every aspect of the game and I think we're more than capable of scoring tries."
Grant spent three seasons with Edinburgh before joining Glasgow and admits he's relishing the chance to show the capital city's followers just what he's been up to.
"I've got a lot of friends at Edinburgh still and it is good to come back and play against those guys and maybe show the Edinburgh crowd that I've not disappeared and that I'm still working hard on the other side of the country," he added.
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