Cohen believes there are too many conflicting demands on finances and players to make expanding the English top-flight viable and says rugby must look at aligning the international seasons, even to the extent of shifting the Six Nations.
Some clubs are campaigning hard for a 14-team league, but Cohen, who reckons expansion could cost the Tigers up to £600,000 per annum, told The Rugby Paper: “I’m against it for two main reasons.
“Firstly, what financial stability there is would be significantly threatened by a move to dividing the money 14 ways instead of 12.
“But my major point is that the game is getting harder and more physical, there are more demands on players and we need to look at structures and processes by which they play fewer matches instead of more.
“Also, if you move to 14 teams, unless you have conferences, which I’m not a fan of, you get to a situation where your England players will be missing significant chunks of the Premiership which would devalue the league.
“There are arguments for and against ringfencing, but arguments against 14 teams are significant and player welfare must come first.”
Cohen believes moving to a global season structure will be key to any expansion. He added: “A modern game needs modern thinking and I’m not sure we have enough of that globally in terms of how we schedule fixtures.
“You should be able to play international tournaments in the North and South at the same time and we need a better season structure, which could potentially entail winter breaks in this part of the world and shifting the Six Nations.
“I don’t know all the answers but I’d be very disappointed if the new heads of agreement with the RFU meant the Premiership had no say in the international calendar beyond 2019.”
Cohen, meanwhile, has expressed concern over the mounting number of fixtures televised live on Saturday and Sunday evenings, particularly European games, which he claims are affecting attendances at big matches.
A number of Premiership clubs are believed to be annoyed and Cohen said: “If you sell your TV rights then TV will want to put matches on at the best time for them, but one thing that will sustain the game is fans in the ground.
“Kick-off times such as 7.45pm on a Saturday night and 5.15pm on Sundays are a significant disincentive for fans to attend live games.
“Crowds have been down at those times and fans tell us that was the sole reason they didn’t go.”