The head teacher of Sandown Bay Academy resigned and the board of governors was replaced earlier this year.
Academies Enterprise Trust (AET) said it intended to merge it with Ryde Academy to make "one great school".
It said falling numbers and the consequent impact on finances had prompted the decision.
Sandown Bay Academy came out of special measures two years ago, but is still seen as underperforming.
Pupil numbers have fallen to fewer than 1,000 from 1,252 in 2012.
In a statement, AET, the biggest academy chain in England, said: "It has been becoming increasingly difficult for the school to fund the teachers and the educational resources needed in order to provide the education we would all want for the students.
"We believe that merger offers the best option all round, and that out of these two schools we can create one really great one."
If approved, the principal of Ryde Academy, Joy Ballard, will oversee the transition between the two schools.
A spokesman said no decision had been made on whether to operate two campuses or on any job cuts.
A public consultation is to be held on the plans, with the final decision made by the government after the general election.
A troubled Isle of Wight academy is set to merge with another school, its sponsor has announced.