Southend United and another League One side are interested in the winger but interest from the Whites may win over the 24-year-old.
United are understood to have made a bid for Morgan and the offer will be considered by Luton's administrators after the club were declared insolvent in November.
Sources at the Bedford club have confirmed that Morgan will be sold this month along with up to four other players as the club fight to keep themselves above water.
Morgan has been on loan at Southend United since the middle of November and the Shrimps have also registered their interest to keep him long-term.
Dennis Wise has been a long time admirer of Morgan, who he attempted to sign last season, and the former Colchester United trainee is also known to Leeds' Andrew Hughes. They were team mates together at Reading.