The 18-year-old took part in the club’s return to training on Tuesday, in a boost as Jamie Godbold rebuilds from a summer exodus of players reacting to relegation.
French, who has two years remaining on his contract, looks set to remain with The Yellows after trialling for both Crystal Palace and Championship side Ipswich Town last season.
Manager Godbold said interest appeared to have temporarily cooled, with no recent approaches made.
“It’s great for us going into a new season and league, to have a player of his quality on the books,” he said.
“He has two years left on his deal and we’ve not had any offers for him.
“So as far as we’re concerned, it looks like he’ll stay with us.
“He’s a great player, really talented, and with a lot of potential — and knows the club and what we expect.
“There was a lot going on at the start of the year, with a lot of interest in him so I’m sure that will reappear at some stage but for now, he remains an AFC player.”
French became hot property in January, as Premier League side Crystal Palace rushed to sign him on the last day of the window.
But they were unable to get a deal concluded before the deadline and have not made a fresh appeal for the teenage star this summer, as expected.
Godbold added: “We’ll see what happens, things can change a lot and there’s still time until the new season, but I’m hopeful of keeping him a while longer.
“We’ve never expected to keep him forever.
“He has progressed so quickly and has the ability to keep going.
“So I’m a little surprised, but happy, that it looks like he’ll be playing for us at the start of the season.”
The youngster’s natural position is at centre-back, but he is comfortable playing anywhere across the backline.
A host of scouts, from clubs believed to include Aston Villa, Sheffield Wednesday and as far afield as Scottish Premiership side Aberdeen, watched French last season.
AFC fans will get their first chance to see their seven new signings in action when the club starts their pre-season fixtures on Saturday, with a double header against Haverhill Rovers (12pm) and Thetford Town (3pm) before a clash against Ipswich Town Under-23s on Wednesday, July 12 (7.45pm).
n See page 94 for details of AFC’s first training session and how it went.