The 19-year-old moved to the Premier League side in January from hometown club Exeter City, making his debut for the Swans earlier this month against Hull City.
Garry Monk's team have already equalled their best-ever points return in the top-flight this campaign, and with five games remaining, Grimes wants to help his new side create history.
"The manager has spoken to us about making history - you can have a football career, you can buy flash cars and flash houses, but there’s nothing compared to making history on the pitch," said Grimes.
"For the fans it would be unbelievable, and it would be just reward for them too.
"Swansea’s fans are different class. One of the massive things for me is the huge support we get for away games.
"A lot of the time that I’ve been part of the matchday squad for away games our fans are louder than the home fans. That is a massive tribute to any club."
Grimes, who led out the Young Lions as they defeated USA 2-1 at Plymouth last month, is already feeling right at home in his new-found surroundings.
"Like Exeter, Swansea is a very family-based club and all the fans want the club to do well, so breaking the points record is something for them to really enjoy," he told Western Morning News.
"I’ve settled into the club and city, so now it’s all about keeping my head down and finishing off this season strongly and starting next season afresh.
"It has been different in terms of training between the clubs. Exeter are in League Two while here I am up against high quality Premier League players, so it took time to get used to that.
"There’s obviously a lot of extra gym work to get my body physically in tune with the rest of the squad, but I’ve got used to that.
Grimes in action for former club Exeter City
"I couldn’t do all that straight away as it was a big jump, and that meant I couldn’t put myself in contention for team selection."
He added: "It’s all about learning as much as I can, and I’ve done a lot of that already.
"I’ve not played a lot with the likes of Gylfi [Sigurdsson], Jack [Cork], [Sung-Yeung] Ki and Jonjo [Shelvey] week in week out, but I’ve learned a lot from them in training. When you have that quality around you, then you have to take as much advice as you can from them."
Grimes will be hoping his performances earn him a spot in Aidy Boothroyd’s squad for the Toulon Tournament in France which starts at the end of May.
