And The News understands that the club are monitoring his Swans situation, while also exploring other options.
Due to his limited game time this term, the 22-year-old could be available for a temporary transfer from south Wales.
Cullen has been restricted to a place on the bench under Russel Martin, and is yet to score in 14 Championship appearances this season.
If the Welshman was to leave the Liberty Stadium in 15 days time, it would be his first experience away from the club after progressing through their youth system.
But Pompey might face stiff competition from their league rivals if they are to make a move.
Alongside the Imps, MK Dons, Fleetwood, and Cheltenham are also allegedly in the race for his signature.
Danny Cowley is actively looking to sign a striker in the winter, with George Hirst and John Marquis scoring six league goals between them this term.
Although Cullen is a name known to the Fratton chief, he’s is keeping an open mind ahead of the January market.
And the Blues are expected to be busy next month, in their quest to enhance their promotion credentials.
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