Fleetwood has finished runner-up six times at PGA Tour events, with the last of those when he missed out on the Travelers Championship in June by a single shot.
“It hasn’t happened for me yet out on the PGA Tour but I would much rather be up there and not quite get it done than not there at all,” said Fleetwood.
“Who knows, maybe this weekend is the weekend and we’ll see, and we’ll crack on from there.
“I’m happy to put myself in with a chance over the weekend. I think that’s exactly where you want to be and keep testing yourself.”
World number one Scottie Scheffler is in the clubhouse at seven under after firing 66.
Englishman Harry Hall’s round of 72 left him on four under – a stroke ahead of Scotland’s Robert MacIntyre, while 2022 US Open winner Matt Fitzpatrick is at two under after a disappointing 71, which contained five bogeys.
The second round will resume on Saturday at 13:30 BST.
