The 19-year-old featured 19 times in MLS for the David Beckham-owned Herons in the 2023 campaign, playing alongside the likes of Lionel Messi and Sergio Busquets.
Allen did lose his starting spot at left-back following the arrival of Jordi Alba from Barcelona, although the youngster still managed to start 14 league games over the calendar year.
The former Fort Lauderdale loanee has also represented his country at youth level in the past, earning five caps for the USA Under-20s, scoring one goal.
According to journalist Paul Tenorio, Allen has flown to England in order to go on trial at Premier League outfit Burnley and Championship side Stoke.
The report claims that the left-back will spend two weeks in the country at the two clubs, with a view to impressing enough to earn a switch to European football.
Allen's current deal in Florida expires at the conclusion of the 2024 MLS season, however Inter Miami have the option to extend the agreement by a further two years.
Consequently, the Herons are in a strong position to negotiate a suitable deal for the defender should the Clarets or the Potters decide to launch a bid for the player's services.
Vincent Kompany's Clarets have been very clear with their transfer strategy since promotion to the Premier League, with the Turf Moor club looking to recruit young talents who possess the potential to grow in top-flight stars.
That plan was quickly put into action during the summer transfer window, with Luca Koleosho and Zeki Amdouni joining from Espanyol and Basel respectively.
Burnley have been low on left-back options since last season's loanee Ian Maatsen returned to parent club Chelsea in the summer, before the Dutchman decided against signing permanently at Turf Moor ahead of the 2023-24 term.
As for Stoke, Enda Stevens is currently first-choice on the left side of Alex Neil's backline after joining from Sheffield United in July, however the 33-year-old cannot be viewed as a long-term solution at the bet365 Stadium.
A potential transfer to England for Allen could be complicated by the fact that the defender would require a work permit in order to join either Burnley or Stoke.
The Clarets welcome relegation rivals Sheffield United to Turf Moor on Saturday in the Premier League, whilst Stoke face a trip down to Devon to face Plymouth Argyle in the Championship.