Rookie Maye has impressed in preseason so far, racking up 66 snaps and going 21-of-34 for 192 yards with one touchdown and no interceptions. He also added seven rushes for 32 yards and one touchdown.
Meanwhile, Brissett, who has struggled with a shoulder injury, started all three games, playing 27 snaps and finishing 5-of-14 for 36 yards with no touchdowns and one interception.
Despite losing two of their three games, including a defeat to the Washington Commanders in their final outing on Sunday, Mayo has been pleased with the form shown by his quarterbacks, especially Maye.
"I would say at this current point, Drake has outplayed Jacoby," Mayo said on Monday in his weekly appearance on WEEI's 'The Greg Hill Show'.
"Now in saying that, we have to take in the full body of work, going all the way back to the spring and beginning of training camp. And we'll see where we end up.
"It's Drake becoming more comfortable with the scheme and more comfortable with the players around him. I don't know how the story ends with Drake's rookie season, but all possibilities are open."
Mayo is set to tell the Patriots who will be playing as the quarterback on Tuesday in their season opener against the Cleveland Browns.
The coach has kept a close eye on his two options throughout the offseason, explaining how everything he has seen over the last few months has played a part in his decision.
"It starts in practice and also in the game, where Drake has played better," Mayo told reporters later on Monday.
"In saying that, everyone wants to know who the starter is going to be. There are multiple factors that have to go into this decision.
"One is the total body of work, whether we're talking about the spring or the entirety of training camp. And I would also say, oftentimes we forget about the overall experience that a guy like Jacoby has, which will also be weighted in the decision we have to make in the near future.
"I'm happy with the way those guys are battling it out. Hopefully, over the next couple days, we can name a starter and get the season rolling."
Maye impressed in their 14-13 preseason loss on Thursday, playing four series as he finished 6-of-11 for 47 yards with a four-yard rushing touchdown.
So far, he has mainly been used as the backup option behind Jacoby Brissett during the Patriots' training camp.
The coach praised Maye's performance, though admitted the offense are yet to find their rhythm ahead of the new season.
"Stepping up into pressure, I thought he did a better job overall with using his legs and really extending plays," Mayo said on Friday.
"[The quarterbacks] have to maintain their composure and get the call to the huddle and get those guys out the huddle and be ready to go. [Maye]'s always been like that in my mind.
"I think the entire offense definitely needs to play and continue to jell, and that's what we're going to do."
The Patriots signed Brissett to a one-year contract in March, and immediately named him as a starter, with his experience proving invaluable.
He has struggled to hit his stride in preseason so far though, finishing 3-of-7 for 17 yards in three series on Thursday, including a costly end zone interception.
With only one preseason game still to play, against the Washington Commanders on August 25, Mayo plans to use both quarterbacks, giving them a chance to stake their claim on the position.
"We have three more days of training camp practices, and it's our job as coaches to evaluate, and the competition isn't over," Mayo added.
"They have to show not only themselves and the coaches [but] also their teammates.
"For me, we always talk about competition, and that's at all spots. Even if Drake beats out Jacoby, he earned that role.
"We don't really take that into consideration when he's ready to go. If he's better than Jacoby, then he'll play, and he'll start."
While Cleveland are looking for a new defensive coordinator after firing Joe Woods, while the Panthers want a new head coach.
There appears little appetite from the Patriots' side to let linebackers coach Mayo leave, however, with a team statement confirming talks on a contract extension were under way.
"The Patriots and head coach Bill Belichick have begun contract extension discussions with Jerod Mayo that would keep him with the team long-term," read a statement released to the media.
Mayo has spent his entire senior career with the Patriots since he was drafted by New England in the 2008 draft.
He retired in 2016 after three successive seasons derailed by injury, but joined the coaching staff in 2019.
New England also confirmed they are on the search for an offensive coordinator after a disappointing campaign saw them miss out on the playoffs.
