Hinchingbrooke Hospital in Cambridgeshire and Peterborough and Stamford NHS Trust have agreed to a review of "organisational form".
Huntingdon MP Jonathan Djanogly said he feared they were "weasel words" for a takeover of Hinchingbrooke.
The hospitals have announced they will be "working more collaboratively".
The trusts said the review would focus on "back office" services, "organisational form" and would also investigate how they could "collaborate clinically".
Hinchingbrooke's chairman Alan Burns said the two trusts would be looking at all possibilities, including a merger.
But, he said: "Because [Peterborough and Stamford] are a foundation trust and we are not, if anything it would be an acquisition not a merger.
"We are looking at making the best use of money without a diminution of services."
Mr Djanogly said proposals to merge "back office functions" at a time when local health services were "haemorrhaging money" were "absolutely to be commended".
"However, to move from that to an outright takeover of Hinchingbrooke by Peterborough is, as far as I and my constituents are concerned, out of the question," he added.
"They say they are going to look at the 'potential organisational form' - at the very best that's NHS techno speak, but at the very worst it's weasel words for a takeover."
Mr Burns said the trusts would deliver its proposed "outline business case" on the hospitals' future by April.
In December, the National Audit Office revealed Peterborough and Stamford Hospitals' debt for 2014-2015 was £38.5 million, while Hinchingbrooke's deficit for the same period was £11.4m.
The Huntingdon hospital was the first in the NHS to be run by a private company, but returned to NHS management in April.
The first NHS hospital to be privately run could be merged with another cash-strapped trust under a move to share services and save money, an MP claimed.