Reach, who spent last season on loan to Preston North End, is reportedly wanted at Molineux.
Reach in action against Wolves old boy Richard Stearman
The Black Country side are said to have enquired over the 23-year-old's availability, with his exit deemed "likely" after Boro's promotion to the Premier League.
However, with Reach expected to cost in excess of £2 million, Wolves would prefer a temporary deal, according to the Express & Star.
And with left side pair Jordan Graham and Michal Zyro due to return from long-term lay-offs next season, a permanent move for Reach is perhaps unnecesary.
Zyro could be out until the New Year
But the Teessiders' capture of Ajax winger Viktor Fischer, not to mention their continued pursuit of Gaston Ramirez, leaves Reach's first team prospects looking bleak at the Riverside.
Fischer is Boro's first signing of the summer
Wolves are set for a busy summer, having finished 14th in last season's Championship, and have already signed goalkeeper Andy Lonergan from Fulham.
Smith could be another arrival from Fulham