The Daily Express is reporting that both the Blues and Southampton are keeping a close eye on the 15-year-old midfielder ahead of a possible swoop next year.
The teenager has recently broken into the first team at Northern Irish champions Linfield and he has already had trials with the likes of Tottenham Hotspur and Manchester City, according to the story.
The same story reports that despite Chelsea FC being currently under a transfer ban, the Blues are exploring the possibility of being able to take Allen on a trial basis.
Norwich and Rangers are two other sides said to be keen to sign the highly-rated attacking midfielder.
Chelsea FC are due to serve the second part of their two-window transfer ban in January after it was handed down to them by Fifa earlier in the year.
The Blues have made a decent start to the new season under Frank Lampard and they currently find themselves in fifth place in the table after eight games.
They will return to Premier League action on Saturday afternoon when they host Newcastle United at Stamford Bridge.
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