Universities should be banned from allowing relationships between staff and students or forced to register them, the regulator has proposed.
The Office for Students said its preferred option was to make universities keep a register of staff-student relationships but that a ban could also be introduced.
The plans are part of a consultation on tackling harassment and sexual misconduct in higher education, which runs until May.
Those covered by the proposals would be “relevant staff members”, such as those teaching students or making their work.
The National Union of Students (NUS) said students may be reluctant to report misconduct by staff out of fear of retaliation.
The consultation by the OfS, the regulator in England, said harassment and sexual misconduct in the sector were “serious issues”.
Previous voluntary guidance issued to universities and colleges had seen “some improvements”, but practices still vary.
Some universities including University College London and the University of Nottingham, already ban relationships between students and staff working with them.
The regulator said staff who fail to abide by the requirements could expect to face dismissal.
“The majority of those working in higher education behave appropriately towards their students,” said OfS chief executive Susan Lapworth.
“But we recognise that there can be a power imbalance in personal relationships that could be exploited by unscrupulous staff to subject students to harassment or sexual misconduct.
“That’s why we’re proposing that certain types of personal relationships should be disclosed, with staff dismissed if they fail to do so.”
Other plans in the OfS consultation include requiring each university or college to publish a document outlining its approach and policies on staff-student relationships and banning the use of non-disclosure agreements that prevent students from talking about their experiences.
The watchdog describes a “personal relationship” as one that involves physical intimacy, including “isolated or repeated sexual activity”, romantic or emotional intimacy, and/or financial dependency.
A spokesperson for Universities UK, which represents 140 institutions, said: “Our members take tackling harassment and sexual misconduct extremely seriously and have been working hard to meet their obligations in this area.
“However, we recognise that there is still work to be done. We look forward to working with OfS so that these proposals will further strengthen universities’ own efforts to ensure student safety.
“It is crucial that any new obligations on universities are proportionate and work for the full range of institutions.”
The consultation on the proposed changes ends May 4.
