Peterborough chief Barry Fry says Celtic are Ivan Toney's "preferred choice" but has warned the Scottish champions that they are running out of time if they want to sign him.
Celtic had a £5m bid rejected for the English striker in July, but he continues to be linked with the club.
Brentford are thought to be the front-runners for the 24-year-old, despite having lost to Fulham in Tuesday night's Premier League play-off.
Speaking to the Daily Mail, Fry said: "Celtic are running out of time now.
"The lad is very close to signing for someone else in the next couple of days.
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"Celtic would have been his preferred choice but they are nowhere near it.
"I heard from Ivan’s agent to say Celtic were coming back.
"That was Sunday evening after their first game but I haven’t heard anything."
Toney has scored 49 goals in 94 games for the League One side.
Neil Lennon's men travel to Rugby Park on Sunday as they take on Kilmarnock in their second Premiership fixture of the campaign, having beaten Hamilton Accies 5-1 in their season opener.
