The tall striker joined Southampton from Belgian side Genk after a prolific spell in the Jupiler Pro League, costing Saints a fee of around £15m.
He could not make an impact on the south coast and was a bit part player as Southampton slipped out of the Premier League and into the Championship.
Onuachu’s stock remains high on the continent and he is expected to depart Southampton this summer.
Bundesliga side Gladbach have now made a firm approach for him, according to Belgian journalist Sacha Tavolieri.
Stuttgart are also keen on landing the striker, but Onuachu is not looking favourably on joining a side that battled against the drop from the Bundesliga last term.
It is claimed that developments are expected soon with regard to the hitman’s future.
Onuachu is likely to be keen to quickly turn the page on what has been a disappointing spell at Southampton, who will be playing Championship football next term.
He scored 16 times in just 19 Belgian league appearances last term as defences struggled to handle him.