The Labour leader said in an interview it would be “impossible” for frontbenchers to keep their roles if they defy the will of the British people and vote against triggering Article 50 on Wednesday.
More than 100 Labour MPs are expected to join the SNP and vote against the motion in just a few days’ time.
- May reveals 'Article 50 is a matter for UK parliament'
- Theresa May heeds warning to Nicola Sturgeon over Brexit
Two shadow ministers have already resigned from Corbyn’s team, with a further seven expected to follow suit this week.
But deputy leader Tom Watson suggested at the weekend they could return “within months” of the vote.
Mr Watson said Labour must adopt a sensible approach to dealing with divisions over the Brexit process.
The Labour leader could let back MPs who rebel over the Article 50 vote into shadow cabinet.
A source close to the Labour leader also told the Telegraph there had been “lots of resignations in the last year and lots have returned”.
Corbyn said in an interview on Sunday there was “no need” for resignations at this stage.
He said: “It’s obviously impossible to carry on being in the shadow cabinet if you vote against a decision made after a very frank and long discussion of the shadow cabinet earlier this week.”
Mr Watson said Labour would have to adopt a sensible approach to healing divisions within the party.
Jo Stevens resigned from the shadow cabinet over her opposition to triggering Article 50.
Shadow Welsh secretary Jo Stevens resigned on Friday over the Labour leader’s decision to impose a three-line-whip over the Brexit vote.
Tulip Siddiq, a shadow home office minister, has also quit – and at least six frontbenchers are reportedly prepared to vote against triggering Article 50.
Theresa May's 12 point Brexit plan Mon, January 16, 2017
It's finally here!
Getty Images 1 of 7
Continued cooperation with the EU to tackle terrorism and international crime.
Labour has tabled a series of amendments to the white paper, including one which would give Parliament to send a final deal back to Brussels if they reject it.
Asked if he expected Labour MPs to vote for the bill even if the amendments failed, Corbyn said: “What I have said is, we would vote to implement article 50, we wouldn’t block it. I’ve made that very clear.”
- Nigel Farage 'worried' Theresa May 'won't progress' on Brexit in 2017
- ‘We DON'T want a referendum’ New independence poll dashes SNP hopes
- Booming Brexit: UK firms plan more trade with the EU