The 34-year-old, regarded as one of the best players not to boast a major title, shot a four-under round of 67 on Saturday to reach one under for the tournament.
Fowler has three top-10 finishes at the Open and is popular with the Liverpool crowds who remember his battle with Rory McIlroy in 2014 when he tied for second.
He received warm cheers again on a rainy Saturday morning as he collected four birdies in a tidy round that underlined his resurgence from a career slump.
But he has not been everyone's cup of tea here, especially those with an allegiance to English football club Leeds United.
Fowler was part of the 49ers group that was investing in the Yorkshire club, along with fellow American Ryder Cup players Jordan Spieth and Justin Thomas, but opted out.
"Other than maybe a "coward" comment here or there, 99.9% are amazing," Fowler said after putting himself in sight of another top-10 finish. "But you deal with that anywhere you go. Same thing in the States.
"The fans over here, it's always fun to come play links golf in front of them. I feel like they have such a great appreciation of golf, proper golf shots."
Fowler conceded it was rare to be heckled about his investment choices.
"That may be one of the first that maybe became public. There might be some other ones out there, but yeah, it is what it is. I'll take it," he said.
While Spieth and Thomas are going ahead with buying into the club that was relegated from the Premier League last season, Fowler said there was no going back.
"No, that's already all done. Hopefully it works out with JT and Jordan being involved. My financial team didn't necessarily advise for it, so we decided to not go forward," he told reporters. "I hope (Leeds) play well and kind of get things turned around."
While Fowler does not rule out investing in a club one day, he is more interested in rekindling his golf career.
Fowler finished in the top five in every major in 2014 but fell to nearly outside the world's top 200 last September and he stopped being mentioned as a potential major winner.
That all changed at the U.S. Open last month when he topped the leaderboard for three rounds, eventually finishing fifth.
He almost missed the cut at Hoylake on Friday, avoiding it by one stroke, but revelled in Saturday's calmer conditions.
A victory charge might be too late as he was still nine shots back from leader Brian Harman. But he is trending in the right direction.
"No matter kind of what happens, we'll still have a good round tomorrow and have a good chance to salvage a good finish out of this thing," he said.
