Manchester City would be interested in signing Raheem Sterling if he were to become available, according to Sky sources.
Tottenham have completed a deal for Cologne defender Kevin Wimmer and he will join them in June, Sky sources understand.
The 27-year-old French-born midfielder, who was a free agent after leaving Birmingham in the summer, has signed a deal until May 2014.
A member of the Taysiders' Scottish Cup-winning team in 2010, Gomis played 180 games and scored seven goals in his first spell at United which covered a four-year period from 2007.
Manager Jackie McNamara said, "I know United fans will have great affection for Morgaro for what he achieved here previously, but I have decided to offer him a contract based on what he has shown me over the last five weeks in training.
"His attitude, application and professionalism has been first class and added to the fact that he has excellent ability makes signing him an easy decision.
"Having him as part of the squad will allow me to select alternative tactics and formations at certain grounds and he brings great experience to the squad.
"This signing is very much about making the squad stronger and the length of deal will allow Morgaro and the club to see how the partnership can develop going forward."
Gomis said: "The opportunity to get back playing at Dundee United makes me very happy.
"After initially being offered the chance to keep my fitness level up, I have been impressed by the quality within the squad and have been welcomed by everyone.
"I have great memories of Tannadice but I want to help create more good times for the club.
"I am happy to sign until the end of the season and I am looking forward to playing in front of the United supporters again. "
A product of Chelsea's youth system, Gomis made his full international debut for Senegal in March 2009 while a Dundee United player.