The Labour leader said he envisages it decreasing if the economy is doing well and enough British workers are trained properly.
He has previously said a Labour government would deliver a “fair” immigration policy and recognised it will “probably be lower”, adding he did not want to make predictions.
In an interview with Andrew Neil on BBC One, Mr Corbyn was told neither he nor the Labour Party were the ones to reduce immigration numbers.
Mr Corbyn replied: “We are in favour of managed immigration when the free movement ends when we leave the European Union.
“We are against people being brought in as wholesale workforces to undermine existing working conditions and workers. There will be managed migration in the future based, based on...”
Mr Neil interjected to ask: “Will you be cutting immigration?”
Mr Corbyn replied: “Based on the economic needs of our society.
“We’ve had Theresa May promising in three elections to make cuts to immigration. I’m making no promises on that.
“What I’m saying is the immigration issue would be dealt with on the basis of necessary family reunions and also the economic needs of the country as a whole.”
Asked if he would try to cut the numbers, Mr Corbyn said: “Well, if the economy is doing well and we train people properly then the need to bring in skilled workers from overseas will obviously reduce.”