Fenlon, who left Hibernian by mutual consent last November following a 1-0 defeat to Hearts in the League Cup, turned out for Linfield as a player between 1994 and 1996, winning two IFA Cups and scoring the winning goal on the final day of the 1993-94 season to clinch the title for the Blues.
St Johnstone boss Wright is believed to have been the Belfast club’s first choice to replace Dave Jeffrey, but has indicated his desire to stay at McDiarmid Park.
Former Dundee United striker Warren Feeney, and Ballymena United boss Glenn Ferguson are also thought to be in the frame for the vacant post at the Windsor Park club.
Fenlon has been out of football since his departure from Easter Road. During his time at Hibs, they suffered a crushing 5-1 Scottish Cup final defeat to rivals Hearts, as well as a 9-0 aggregate defeat in the Europa League qualifiers at the hands of Swedish side Malmo, including a humiliating 7-0 loss at home.
If Fenlon takes the post he will be reunited with former Hibs winger Ivan Sproule, who joined Linfield at the end of last year after leaving Ross County, citing personal and family reasons.