United have reportedly agreed a deal of around £12million-a-year to have the dating application advertised throughout the 2017/18 season.
The Premier League has changed sponsorship regulations this summer to allow teams to brand an extra company logo on their kits, providing it is limited to one sleeve.
The other sleeve would still feature the Premier League logo.
United would become the tenth team to sign a deal with a shirt-sleeve sponsor – but no others will have signed a deal worth as much as the Red Devils’ agreement.
The Daily Mail report that a £12million offer is on the table from Tinder, who began their foray into sport last season.
Tinder already has an agreement with Serie A side Napoli, which saw striker Arkadiusz Milik feature in promotional videos.
Industry chiefs are said to value the shirt-sleeve sponsorship at about 20 per cent of that on the front of the shirts.
United currently earn £50million every season from their deal with American car giant Chevrolet.
Tinder is the world’s most popular dating app with over 50million active users and one billion swipes per day.