"I don't believe the House would accept that," he said.
If the full Senate passes the pay raise bill, it will have to return to the House for members to consider the changes. If delegates didn't agree with the changes, the two chambers likely would convene a joint committee to forge a compromise.
Kessler said the two finance chairmen, Delegate Harry Keith White and Sen. Roman Prezioso, met on Wednesday to work out a deal.
Kessler was not sure what came of that meeting but said the Senate had not struck a "quid pro quo" deal with House leaders on the special tax district and magistrate pay bills.
Getting the TIF district bill past the committee stage in the House was a victory for WVU Athletic Director Oliver Luck. Hoping to build a new baseball facility, Luck has been lobbying for the TIF district for over a year.
An attempt to approve the district last year died in the Senate after lawmakers learned developers had not yet submitted required paperwork regarding the proposed district to the West Virginia Development Office.
WVU and Minor League Baseball officials on Wednesday said the district would be a great benefit to Morgantown, enabling them to build a first-class facility.
Mike Parsons, WVU deputy director of athletics, said last month the special tax district would be a major economic engine.
"I think what it does is it provides more than an opportunity for WVU to play baseball. It's more for the community," Parsons said.
"It helps socially and it helps economically just expanding from the three months we'd be using it and when we use it again in the fall. Basically, we're playing a championship season in March, April and May, but this expands the season and the use of it so it brings more of an economic impact to the community."
Parsons made the comments during a March 26 press conferences in Morgantown with Pat O'Conner, president of Minor League Baseball, and Ben Hayes, president of the New York-Penn League, which would bring one of its teams to Morgantown if the stadium were built
O'Conner said, "You're creating a destination not only for athletic events, but for entertainment, shopping, dining.
"You're creating a destination for multiple purposes that sustain the TIF and that sustain the area and promote further growth there."
Hayes said location and fan amenities are the most important factors for the stadium.
"You want to create a good fan experience," he said. "So I would say location and ease of access off the interstate are key things to look at.
"This particular location is ideal in the sense that if you look at the traffic nearby, I believe the road up to there is 20,000 cars a day, which is fantastic.
"In a nutshell, the location in Morgantown is looking like it's ideal for WVU as well as Minor League Baseball."
Sportswriter Mike Casazza contributed to this story.