Labour leader Jeremy Corbyn said he is considering the idea, while Leader of the House Chris Grayling said MPs should “do what they feel comfortable doing”.
Parliament has been recalled on Monday to allow MPs to remember Ms Cox, who was killed in her constituency of Batley and Spen in West Yorkshire on Thursday.
Neighbouring Labour MP Jason McCartney, who represents Colne Valley, has written to Speaker John Bercow requesting that backbenchers be permitted to sit together across the House in a mark of solidarity.
Asked about the idea on the BBC’s Andrew Marr Show, Mr Corbyn said: “I received that suggestion last night actually and we’re thinking about that and have a talk tomorrow, but tomorrow is going to be a dignified occasion, it’s not going to be a time for lots of long speeches.”
He added: “An MP has died. It’s an attack on all of us. In her memory we have to create a more tolerant society. In her memory we have to reach out.”
Asked about the rules of the house, Chris Grayling, leader of the House, told Sky News’ Murnaghan: “I don’t think there are any formal rules but I think for tomorrow’s event it is a celebration and a commemoration and an expression of profound sadness and to my mind it is an occasion where people should do what they feel comfortable doing.”
Meanwhile, leader of the Liberal Democrats Tim Farron said it is a “great idea” and would show that MPs are “united against hate”.