Celtic set to beat Tottenham Hotspur in midfielder race
The Hoops are understood to have offered the 15-year-old the chance to come and train at Lennoxtown ahead of making an offer.
Spurs were believed to have stolen a march on their rivals by offering Allen a trial - Liverpool, Manchester United, Manchester City, Leeds and Leicester were all monitoring the teenager's progress.
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Hide AdThe champions added two youngsters to their development squad last month, bringing in goalkeeper Tobi Oluwayemi and Norwegian defender Leo Fuhr Hjelde on three-year deals.
Allen has already made his debut for Linfield, and is a Northern Ireland Under-17 international able to operate at centre-forward or as an attacking midfielder.
He would almost certainly play in Celtic's reserve side to begin with but given Neil Lennon's tendency to reward highly-rated youngsters could see Allen handed a spot in the first-team squad in the not-too-distant future.