Forest's sporting director joined them in February this year, having previously held a similar role with Watford.
Albion's Championship rivals were bought by Greek shipping magnate Evangelos Marinakis in May and their recruitment over summer has leaned heavily on super-agent Jorge Mendes.
And despite being at Forest for just seven months, Dowling has emerged as a potential target for the Baggies, who are believed to have made contact.
Albion chief executive Mark Jenkins has begun to focus on appointing a new technical director since the loan window shut last week.
He flew out to China earlier this week to speak to owner Guochuan Lai about filling the role.
Dowling is a former academy player at Tottenham Hotspur who also played for Reading before injury cut short his career at 28.
He started scouting for AFC Wimbledon part-time before subsequently working for Crystal Palace, Portsmouth and Leeds.
During his time with Portsmouth he worked alongside former Albion player Michael Appleton.
In 2014 he was appointed Watford sporting director, and during his three years at the Hornets he helped take Etienne Capoue and Abdoulaye Doucoure to Vicarage Road.
He left the club by mutual consent in August 2017 before Forest appointed him in February this year.
The Baggies are looking for a technical director after Lai sacked Nick Hammond from the role in April for his influence in appointing Alan Pardew as head coach last season.
Albion’s Chinese owner then appointed Giuliano Terraneo has a temporary technical consultant for the summer, but his stint was cut short due to differences behind the scenes with both Jenkins and head coach Darren Moore.
Jenkins is eager to have a technical director in place in time to prepare for the January transfer window.
Meanwhile, the Baggies are also reportedly contemplating handing free agent Wes Hoolahan a trial in the coming days.
Moore’s players are due back in for training tomorrow after a few days off at the beginning of the international break.
Playmaker Hoolahan, 36, was released by Norwich in the summer after 10 years with the Canaries.