The powerful forward is well known to Baggies technical director Luke Dowling – with the pair having previously worked together at Watford.
A Senegal international, Niang is understood to want to return to the Premier League and was left out of the Rennes squad which took on Monaco over the weekend.
After beginning his career with French outfit Caen, Niang moved to AC Milan in 2012 for an undisclosed fee.
Aged 17 years and 350 days, he became the Italian giant's youngster ever goalscorer when he netted in a Coppa Italia game against Reggina.
Loan spells at Montpellier, Genoa, Watford and Torino followed before he joined Rennes permanently in 2019.
Niang has scored 21 goals in 57 outings for the French side.
But he has also made headlines for the wrong reasons in his career.
He received a suspended 18-month jail sentence when he crashed his car into a tree – injuring 11 people – while on loan at Montpellier.
He also broke a curfew while on international duty with the French Under-21 side and has since switched his allegiance to Senegal.
The Express & Star understands Huddersfield's Karlan Grant remains Albion's preferred choice as they work to bring in a striker.
A loan deal for Watford's Andre Gray is also being considered.
But with funds at The Hawthorns tight, Niang is now under serious consideration as Slaven Bilic looks to add more goals to his squad.