Scott told TMZ Sports he wants the team to remain in Tampa.
The Major League Baseball executive council gave permission to the franchise to explore becoming a two-city team last week. The tentative plan was to split the season schedule between the Tampa Bay area and Montreal.
"There is no commitment on the part of the owners to ultimately approve a plan," Manfred told reporters Thursday. "The permission that was granted was simply a permission to explore this alternative in an effort to strengthen a franchise that has performed great on the field but continues to be pretty limited from an economic perspective."
Scott, the former governor of Florida, said he'd like the Rays to "spend all of their time in Tampa."
"Look, Montreal is a beautiful city," Scott said. "I've enjoyed the times I've had the opportunity to visit there. But I hope Tampa spends all their time in Florida."
St. Petersburg Mayor Rick Kriseman expressed a similar sentiment last week, saying the ultimate decision is up to him.
"The Rays cannot explore playing any Major League Baseball games in Montreal or anywhere else for that matter prior to 2028 without reaching a formal memorandum of understanding with the city of St. Petersburg," Kriseman wrote Friday in a Facebook post.
"Ultimately, such a decision is up to me. And I have no intention of bringing this latest idea to our City Council to consider. In fact, I believe this is getting a bit silly."
The Rays are committed to Tropicana Field through the 2027 season, according to MLB commissioner Rob Manfred. A source told MLB.com that the team views 2024 as the earliest possible date for a potential split season between ballparks.
The Rays have played at Tropicana Field since 1990 and have been trying to obtain a new stadium for several years. Manfred said the specifics of the Rays future plans will be determined by what owner Stu Sternberg works out with MLB's other owners.
Sternberg released a statement Thursday, saying his priority is to keep baseball in Tampa Bay "for generations to come." Sternberg also said he believes the concept of playing in another city "is worthy of serious exploration."
The Rays sit in second place in the American League East with a 45-33 record, five games behind the New York Yankees. Tampa Bay hasn't won the division since 2010.