The party is in open conflict following Britain's vote to leave the European Union on Thursday. Labour's widely respected foreign policy chief Hilary Benn was sacked earlier after saying he had lost confidence in Corbyn.
"I think that there are a fair number," Alexander told ITV television in response to a question about how many of her colleagues she expected to resign.
"I know from the conversations that I've had with colleagues that this is a very difficult time for all of us. It's not a decision that we want to take but some of the time you do have to take tough decisions in politics and so I know a lot of my colleagues will be asking themselves similar questions to the one I've asked myself this morning."