Labour Deputy Leader Tom Watson has urged colleagues not to split and form a rival party.
Mr Watson, MP for West Bromwich East, said: “It would be a very sad and disappointing day if there is a breakaway.”
And he said of unhappy Labour MPs: “I hope they can stay and fight their corner.”
There has been speculation about Labour MPs forming a breakaway party since Jeremy Corbyn was elected leader in September 2015.
But that speculation has grown significantly since Christmas, with reports that at least six Labour MPs are ready to announce the formation of a new party.
Reports have suggested that Labour MPs including Angela Smith, former shadow chancellor Chris Leslie and Luciana Berger may be involved.
Unhappiness with Jeremy Corbyn among some Labour MPs has come to a head because of his perceived unwillingness to take action against anti-semitism in the party; his failure to speak out about events in Venezuela, where the Government is locked in a battle with opposition forces, and stalling over whether or not to back a second Brexit referendum.
Labour’s conference voted last year that supporting a so-called People’s Vote would be “on the table” if Theresa May’s proposed Brexit withdrawal agreement was rejected by Parliament, and if Labour was unable to secure a general election.
But Labour has still to make a decision about whether or not to back a second referendum, even though the deal was overwhelmingly rejected in a House of Commons vote on January 15, and there is no sign of a general election.
Some senior figures, including Mr Watson, have suggested that Labour will announce it backs a second referendum if Prime Minister Theresa May rejects Mr Corbyn’s offer to work with her on Brexit. But Mr Corbyn has shown no sign of endorsing this view.
Speaking on Pienaar’s Politics, on BBC Radio 5 Live, Mr Watson said: “I hear the rumours ... I’ve been hearing them for about a year.”
He added: “As a member of the Labour Party for 35 years, I genuinely want people to stay in the party, to hold together, to fight for an electorally-viable party. One that has a programme that addresses the issues of concern for the future.
“Beyond Brexit, we’ve got 9 million jobs threatened by artificial intelligence. So what I’ve said – and I said it at the conference as well – I hope they can stay and fight their corner.
“And it would be a very sad and disappointing day if there is a breakaway.”
And speaking on BBC One’s Andrew Marr show, he admitted: “I am worried about it.”
Mr Watson said: “I hope people will stay and fight their cause. You know, because an electorally viable Labour Party addressing the issues that the future economy is going to bring workers in this country is always the best vehicle for social change.”
Labour split in 1981 when the SDP was formed senior Labour MPs who were opposed to what they saw as the leftward drift of the party under then-leader Michael Foot.
The SDP enjoyed some success, gaining 25.4% of the vote in the 1983 general election, although it only won 23 seats out of 650 contested.
Some commentators believe the SDP helped the Conservatives, led by Margaret Thatcher, win a landslide victory, by splitting the left and centre-left vote.
The party eventually merged with the Liberal Party to form the Liberal Democrats.