The 19-year-old — who honed his skills as a youngster at Sporting Lisbon's academy — secured a switch to the Dutch giants in the summer for around £10m from Manchester City.
Forbs caught the eye of Ajax with a goal-laden season for the Citizens' Under-23s side, scoring 21 times in 24 Premier League 2 appearances last campaign.
The attacker also possesses international pedigree, having represented Portugal Under-21s on three occasions since making his debut at that level in August.
After just six months in the Netherlands, Forbs could be readying for a move back to England, with Football Insider reporting that Burnley are in discussions for the player.
It is understood that Ajax are open to letting the Portuguese depart on a loan deal for the remainder of the campaign, as the attacker has fallen down the pecking order under John van't Schip.
Forbs has appeared in 16 Eredivisie matches this term — starting only six of those — scoring once and providing three assists in a total of 613 minutes of league action.
Vincent Kompany is said to be a huge admirer of the former Man City man, however the Clarets are not alone in their interest for the winger.
It is believed that relegation rivals Nottingham Forest have also been in contact with Ajax over a deal for Forbs, who reportedly wishes to prove himself in the Eredivisie following a hit-and-miss start.
Burnley have already strengthened in attacking areas during the January transfer window, securing the services of Chelsea's David Datro Fofana on loan for the remainder of the season.
The ex-Molde striker spent the first half of
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