Former shadow business secretary Clive Lewis has also written to the advisory committee on business appointments (Acoba), saying the committee should rebuke Osborne for accepting the post before he had written to the committee for guidance.
Osborne, a Conservative lawmaker, was the chancellor of the Exchequer in prime minister David Cameron's 2010-2016 government, dealing with the aftermath of the global financial crisis.
The MP for Tatton now has a total of six highly paid jobs including his constituency work, as editor of the Evening Standard, chair of the Northern Powerhouse partnership, an adviser to BlackRock, academic work as a Kissinger fellow in the U.S., and an after-dinner speaking contract.
The rules on MPs taking second jobs could be changed after George Osborne's appointment as editor of the London Evening Standard, the chairman of the country's chief standards watchdog has said.
Separately, Paul Bew, chairman of the United Kingdom advisory Committee on Standards in Public Life, said he was "uncomfortable" with Osborne's professional arrangement and that it was the right time to "discuss whether our rules on second jobs need to be changed in light of this", according to the newspaper.
"We have not ruled out MPs having second jobs, quite deliberately, up until now, but we now have to look again at our rules. Now it seems to be getting into rockier waters".
Following the recent reduction in the Evening Standard's print editions, Osborne apparently believes he can edit the newspaper in the morning and attend parliament and do his collection of other jobs and lucrative speaking engagements in the afternoons and evenings, much to the disbelief and private derision of the paper's journalists, a source said.
Tommy Sheppard, an SNP MP on the committee, told The Telegraph he would push for two new rule changes to the code of conduct next month.
One pilot dead after two small planes collide near Montreal
One eyewitness, Carol Pelchat, told the news channel that she heard two planes overhead when she came out of the shopping mall. Cargair said in a news release it was working with authorities and offered its sympathies to the families of the pilots.
He said: "You can not edit the Evening Standard and represent your constituents in any meaningful sense".
'How many votes would you miss in the Commons, for example?
Ruth Davidson, who worked as a BBC journalist for many years before entering politics, said she could not see how the former Chancellor would have time for both jobs.
"Why not? He is a highly capable guy and it should make politics more interesting."
Stephen Kinnock, Labour MP said on ITV's Robert Peston Show: "When I first read this I thought it was fake news and sort of choked on my cornflakes".
"I wouldn't be letting someone else do it and I just don't think it works. So I'm not sure you could do both at the same time, if I'm honest".
"Frankly George Osborne will provide more effective opposition to the government than the current Labour Party".
Evgeny Lebedev, proprietor of the newspaper, said: "In George, we have appointed someone of huge political achievement, and economic and cultural authority".