The Sheffield United legend has wasted no time getting used to life in the States after signing for LA Galaxy in the summer.
His latest performance saw the 37-year-old score a match-winning hat-trick against Minnesota United in a 4-3 victory for the Galaxy.
And speaking to The Athletic, Sharp took a pop at Wrexham after helping Sheffield United knock them out of the FA Cup last season.
With the latest episode of 'Welcome to Wrexham' set to be released, he said: "If they want to put me in the documentary, go ahead.
"I think people in Los Angeles probably know me now for scoring goals rather than knocking [Wrexham] out of the FA Cup.
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"People don't even know the real story. Wrexham will put out what they want to on their documentary, and maybe I'll put out my own and tell them what really happened."
When Wrexham drew Sheffield United in the FA Cup, no one saw the resulting drama - a 3-3 draw where John Egan netted a 95th-minute equaliser saw the match go to a replay, which the Blades won 3-1.
Sharp scored in the 94th minute before Sander Berge grabbed another seconds later to confirm the result in a rollercoaster tie, though there was more carnage to come when the striker got into a mini-scrap with Wrexham boss Phil Parkinson.
"I scored the goal, which knocked them out, and a little scuffle happened in the changing room," Sharp continued.
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"I don't really like their manager anyway from past experiences, and he probably doesn't like me.
"It's just one of those things in football where it sometimes gets very overheated… I know what they're going to do; they're going to show the clips that make me look like a baddie.
"That's fine. I'll wait to see what happens and have my say afterwards. The record book says we beat them in the FA Cup, so they can have a documentary about it if they want."
Sharp is an undoubted legend for the Blades, having played for them three times after coming up through their academy, but his eight-year spell came to an end this summer.
He made the surprise move to the MLS where he has hit the ground running, netting six times in six appearances already.
LA Galaxy have signed superstars in the past including David Beckham, Steven Gerrard and Zlatan Ibrahimovic.
But Sharp is already a fan-favourite, even earning his own song already - to the tune of 'Baby Shark'.
"I don't understand it," the 37-year-old said. "I'm sure the tune of the song that Sheffield United fans used to sing was an American song ['Give it Up' by KC and the Sunshine Band].
"If that's what they want to sing, that's fine. They've been really supportive of me. I don't think they really want to sing that because it's kind of half-hearted.
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"They're just trying to get behind me, which I'm obviously thankful for. It did happen in England, but it soon stopped.
"Listen, I'm not overly fussed, but if they sang the other one… yeah."