Southampton were previously rumoured to be leading the Premier League chase for the 24-year-old before he was linked heavily to United over the weekend.
Saints boss Ronald Koeman said: "We are interested in Rojo but the transfer is a question for the chairman and (executive director) Les Reed."
Rafael Benitez's Napoli are interested in taking Rojo to Serie A but new United manager Louis van Gaal is thought to want cover and competition for England left-back Luke Shaw, 19, at Old Trafford.
Rojo did not train with Sporting on Tuesday but United have yet to comment on reports in Portugal which suggest a £16million offer has been lodged for the World Cup runner-up.
Sporting president Bruno Carvalho has confirmed Rojo and team-mate Islam Slimani will be disciplined for missing training and will not be involved for this weekend's clash with Academica.
Carvalho also vowed that Sporting will not be forced into selling both players before the close of the transfer window.
"They will not play on Saturday, against Academica. Nothing is at stake here," Carvalho told the club's official website.
"Let’s see how long their disciplinary procedure will last. It will not be finished by Saturday.
"Both players made decisions that caused indiscipine inside the club. Right now, they face disciplinary action.
"They still have three years left on their contracts.
"Players have expectations, and Sporting will always try to see what can be done about that. But we will not give yield to pressure from agents and funds, we will not yield to attitudes that disrespect the club."