James Duddridge said the Zimbabwean president should be given a "soft landing" outside the country to allow a "less bloody" transition.
But he stressed any interim government must only be in place for a relatively brief period rather than a "faux" unity regime seizing power.
The Conservative MP, who was responsible for Zimbabwe at the Foreign Office between 2014 and 2016, said he would try to press Theresa May on the issue at Prime Minister's Questions on Wednesday.
He will look for answers on what support the UK can provide to civil institutions that have been "ripped apart" under Mugabe, and said he hoped diplomatic, political and economic help would "flood in".
But he stressed it would be inappropriate for the UK to support a coup, as Zimbabwe's army detained Mugabe and his wife Grace and secured government offices after a night of unrest in which it took over the state broadcaster.
Mr Duddridge told the Press Association: "I intend to try to catch the Speaker's eye and raise a question at Prime Minister's Questions to ask what economic and physical support we can give, because the civil institutions of Zimbabwe have progressively over the last 40 years been ripped apart.
"And I would hope that the UK has a plan to deal with this type of scenario to flood in extra political support, diplomatic support, but also crucially economic support to allow that country to prosper.
"The British Government should support the Zimbabwean people to bring the whole thing to a conclusion and chart a way forward.
"It is for the Zimbabwean people to chart a way forward, not Her Majesty's Government.
"But I think they are doing that, they will do that, and we will support them coming out of what has been a rather nasty dictatorship by one man to a slightly more functioning democracy, probably transitioning by a government of national unity.
"But it may very well be that we need to provide support in the transition to maintain stability - that is in the Zimbabwean people's interests, it is in the British national interest."
Mr Duddridge, who worked as a banker in Swaziland and Botswana, which neighbour Zimbabwe, and was secretary of the all-party parliamentary group on Zimbabwe, said it was a "crucial time" for the country and region.
He said Zimbabwe, formerly known as the breadbasket of Africa, could again be a "powerhouse" in southern Africa "if it regenerates democratically and economically".
"So I very much hope for a bloodless and peaceful transition from an autocratic dictator, who has served his time and needs to move on, to a more democratic, open nation state that will trade and prosper and start to rejuvenate the Zimbabwean people.
"There's always a concern when there's a transition of power but we must remember Mugabe is loved by many people around Africa as a revolutionary leader.
"But he's morphed from that into a rather distasteful dictator who has abused his position.
"Providing Mugabe with a soft landing outside of Zimbabwe which, whilst is distasteful given everything that he has done and has been done in his name, will allow for a less bloody transition."
Shadow foreign secretary Emily Thornberry said: "The situation in Zimbabwe remains highly volatile, and we urge the UK Government to continue providing every assistance necessary to British nationals currently in the country.
"Amid the uncertainty of these ongoing events, three things are clear: first, a descent into violence, recrimination and reprisals from any direction must be avoided at all costs; second, the continuation of authoritarian rule does not represent a sustainable way forward for Zimbabwe, no matter which faction ends up in control; and third, it must ultimately be for the Zimbabwean people to determine their own future government through free, peaceful and democratic elections."