Transport for London (TfL) has applied to take over the services of Tube maintenance firm Metronet, which went into administration last month.
Metronet went into administration after a projected £2bn overspend
It follows the announcement of a series of London Underground strikes over job losses faced by Metronet staff.
Metronet planned to invest £17bn in the Tube but went into administration amid serious financial problems.
TSSA union general secretary Gerry Doherty said the TfL bid was "a very positive development".
Metronet is responsible for the upkeep of nine Tube lines, including the Bakerloo, Victoria and Central, and was hired under a private-public partnership (PPP) scheme.
It was involved in a long-running dispute with Transport for London about who should pay for the spiralling cost of upgrading the network's infrastructure.
TfL expressed an interest in running the services on a temporary basis to the Metronet administrator on Friday.
A day earlier members of the Unite and Rail, Maritime and Transport (RMT) unions announced they would hold 72-hour strikes on 3 and 10 September.
A 48-hour strike by the Transport Salaried Staffs' Association (TSSA) is also planned on 4 September.
RMT general secretary Bob Crow said Metronet's Tube staff "will not accept being made to pay for the failure of the PPP and the decision by Metronet's fat-cat shareholders to walk away from the contract".
He added that strikes would "disrupt the entire (Tube) network" as they could result in a lack of staff to carry out vital track maintenance and safety checks.
TSSA general secretary Gerry Doherty said: "Returning Tube maintenance to TfL could ultimately deliver a stable, economic and efficient structure that is better able to meet the needs of Londoners than that delivered by the failing private sector under the PPP arrangements."
A TfL spokesman said it would submit its formal application to run Metronet's Tube maintenance service at the end of September.