A three-day training camp in Teddington, Middlesex, was due to finish on Monday, with Tuilagi the standout inclusion, having not played for his country since March 2016 due to injuries.
It has been reported in several newspapers that Tuilagi and Solomona, who trained on Saturday and Sunday, went out on Sunday evening and drank alcohol, contravening the team's cultural standards.
No decisions have been made as to what will happen to them after the three-day get-together and the RFU said that it would not be making any further comment.
Tuilagi has made one appearance under England head coach Eddie Jones, in the 2016 Six Nations Championship, and last started an international in June 2014.
Rugby league convert Solomona, meanwhile, made his first appearance for England during the recent tour of Argentina, scoring the winning try in the 38-34 first Test victory.