Friends and colleagues of the late Mo Mowlam want a permanent memorial to be created close to the former Redcar MP's Teesside home.
Ms Mowlam received an honorary degree at Teesside University
Ms Mowlam, who was Redcar MP from 1987 to 2001, died on Friday aged 55.
She was admitted to hospital following a fall at home and never regained consciousness. She had previously suffered a brain tumour.
Options being considered are a statue close to her Teesside home, an annual lecture or scholarship in her name.
Vera Baird, who took over as Labour MP for Redcar, said the people of Teesside were still mourning the former Northern Ireland secretary.
She said: "My sadness at the loss of Redcar's own Mo Mowlam continues.
"It is understood that the funeral will be private, but Labour councillors propose that there should be a memorial event in the constituency, a place which she loved and where she was married almost 10 years ago.
"In addition they will initiate a permanent memorial, probably to be placed on the Esplanade opposite her former home.
"I would be very keen that Redcar people should make suggestions as to the form it should take, whether a statue of her or some significant artefact which reminds us of the great woman we have lost.
"Following discussions with colleagues and friends over the weekend, I will take steps to found a Mo Mowlam Memorial Lecture. It should take place annually on Mo's birthday in September."
Redcar and Cleveland's mayor Peter Spencer echoed calls for a permanent memorial.
He said: "It's important that we try and involve as many people as possible in any decision on a permanent tribute for Mo.
"I'm sure there will be support for a memorial service and I will be talking to the mayor's chaplain about what sort of form that could take.
"It will also be important to talk to Mo's family and involve them in any final decisions we take."