Shwe Mann was sacked from the Union Solidarity and Development Party (USDP) last week in a power struggle.
He has been rumoured to be discussing an alliance with Aung San Suu Kyi whose party is expected to win wide popular support in the 8 November elections.
They will be the first elections since democratic reforms began in 2011.
Rivalry between President Thein Sein and Shwe Mann came to a head last Wednesday night when trucks with security sealed off the headquarters of the party.
Shwe Mann, who had been seen as a likely successor to Thein Sein, remains speaker of parliament and a USDP member.
Ms Suu Kyi and Shwe Mann met for an hour on Monday in the country's capital, Naypyidaw.
They have often said that they have a mutual understanding for future co-operation, reports Moe Myint of the BBC Burmese service.
One likely area of collaboration might be amendment of the constitution, which prevents Ms Suu Kyi from running for the presidency.
Most expect Ms Suu Kyi's National League for Democracy to win the election, but the constitution bars her from becoming president because her children hold British passports.

The council is consulting on plans to introduce a cycle lane on Pontcanna's Cathedral Road, make some streets one-way and removing a traffic island.
It comes as part of the 2015-16 local transport plan, which proposes new cycle lanes across the city, 20mph speed restrictions, crossings and park and ride improvements.
The council aims for 50% of trips to be made by sustainable modes by 2026.
The Cathedral Road project is part of a wider north west Cardiff bus corridor scheme, to improve journey time and reliability so more people are encouraged to use buses.
The council estimates Cardiff's population will increase by nearly a quarter over 25 years, resulting in a 32% increase in traffic and 20% increase in commuters.
The plans include measures to re-allocate space on the roads to cyclists and remove on-street parking on the approach to junctions. There are also plans to add bus lanes and improve signage.
The former chairman of Myanmar's ruling party has met opposition head Aung San Suu Kyi, prompting speculation of an alliance.
[NEXT_CONCEPT]
Major overhauls to transport routes in Cardiff are being considered.