London have struggled to attract crowds at The Valley
The Northern Ford Premiership club became interested in the venture after revelations that Broncos' sponsor, Virgin, is ready to pull out because of large financial losses.
York, who finished bottom of the NFP last season, are now competing with Leigh to wrest control of the Super League franchise.
But one obstacle to the bids will be the Rugby Football League and Super League's desire to keep a top-flight presence in the capital.
If York were successful in purchasing Virgin's majority share-holding, the merged club would be re-located to Huntington Stadium under a new name, York Wasps Ltd.
York vice-chairman Russell Greenfield confirmed the bid.
"We have made an approach to Virgin and asked them for a meeting next week," he said.
"We would certainly be interested in buying their shares.
"We have written to Chris Caisley (chairman of Super League) and Sir Rodney Walker (chairman of the RFL) to inform them of our intent."
Plans for next season
York, who won only one of their 28 fixtures last season, are determined to prove that they are up to the task.
The club plan to unveil a major sponsor and new coaching team on 18 September.
York have also said they would be able to upgrade their Huntingdon Stadium to make it suitable for Super League.
But Broncos commercial director Nick Cartwright said he was unaware of any talks with other rugby league clubs.
Cartwright said that the only ongoing negotiations that he knew about were between the club's board of directors and Charlton Athletic.
"There is a determination to stay in London with Virgin support, that is the number one aim," he said.
"I would imagine that all will be resolved by the end of the season."
RFL director of rugby Greg McCallum said he fully supported Super League chairman Chris Caisley's desire to see the Broncos remain in the capital.
"From a strategic viewpoint, losing London would be absolutely devastating," he said.