The announcement comes following an incident in the early hours of Monday morning involving Celtic goalkeeper Lukasz Zaluska.
The Scottish Premiership club have released a statement saying that two of their players, both of whom will be unavailable for selection this weekend, are part of an internal probe.
According to the Evening Telegraph, Wilson and Paton were in the Glasgow area at the time when Zaluska, who spent two years at United before joining Celtic in 2009, was allegedly assaulted by a fellow Premiership footballer.
Reports have claimed that the Polish shot-stopper was hospitalised with a head injury, but has since returned to training.
A statement on United's official website said: "Dundee United Football Club has commenced an internal investigation into the conduct of two of its players following information received by the club. The club will make no further comment at this stage."
Manager Jackie McNamara is unable to say if the club's investigation is in relation to the incident involving Zaluska.
Police are investigating the alleged assault and no arrests have been made.