"I'd love to [give Malcolm the truck]," Brady said on Boston sports radio station WEEI. "We're going to figure out how to make that happen."
Butler, an undrafted rookie out of West Alabama, became the Patriots' unlikely hero when he made the Super Bowl-winning interception on a Russell Wilson pass intended for Ricardo Lockette at the 1-yard line with 20 seconds remaining in the Patriots' 28-24 victory over the Seattle Seahawks.
"It's an incredible play, and not only that, that's the type of plays Malcolm makes for our team," Brady said. "A guy like Malcolm who makes that type of quick, instinctive plays, that's one of his strong suits. I don't think it surprised any of us players because that's what his skill set is."
Brady has won three Super Bowl MVP awards, tying Joe Montana's NFL record. So Brady can spare the truck that came with the Super Bowl XLIX honor.
"A lot of people didn't get to see [Butler's skills] throughout the course of the season," Brady said. "[Butler's interception] comes off as a great play, which it really was, at the biggest time of the year."
Butler said in an interview with ESPN Radio's "Mike & Mike" on Monday morning that his work in practice helped him to recognize the play.
"At practice, the scout team ran that same play and I got beat on it. [Coach] Bill [Belichick] told me, 'You've got to be on that.' At that time [of the play], memorization came through," he said. "I just jumped the route. I just made a play. Just do your job -- do it the best way you can. I just did my job."
The rookie safety took to Twitter on Tuesday after a whirlwind two days.