According to Sky Italia, the Giallorossi are offering a loan worth β¬5m with an obligation to buy set at β¬35m, a structure Gianluca Di Marzio reports Stuttgart have rejected as an opening position.
AS Roma are said to be dangling a five-year contract to help persuade the 25-year-old, whose versatility across the front line has made him one of the more sought-after wingers in the Bundesliga this season.
Roma are far from the only club interested. Inter Milan have also been credited with scouting Leweling, while Everton and Liverpool are both mentioned among the English clubs to have made enquiries - Everton's interest carrying particular intrigue given the club shares ownership with Roma under the Friedkin Group.
VfB Stuttgart, whose finances depend heavily on generating transfer income this summer, have not ruled out a sale of their Germany international, but Roma will need to significantly improve their offer if they want to convince the Swabian club to let him leave before the market closes.
Leweling joined Stuttgart from Union Berlin in 2023 and has since become a key figure in their attack, forcing his way into Germany's national team picture along the way. Losing him would represent a significant blow to Stuttgart's forward line, but with the club under pressure to balance the books, a departure this window cannot be ruled out if the right offer eventually arrives.
Leweling scored 11 goals and provided 12 assists in 50 appearances across all competitions last season, form that has continued to attract admirers well beyond Roma. Bournemouth had an earlier β¬40m bid rejected in the winter, while Stuttgart's own valuation is understood to sit closer to β¬50m - a figure Roma's current loan-plus-obligation package falls well short of.
With Leonardo Balerdi already arriving at Roma on a separate loan deal from Marseille, manager Gian Piero Gasperini remains keen to add a genuine wide threat to complement his 3-4-3 system before Tuesday's deadline.