A decision deadline is rapidly approaching.
Mesa officials have scheduled a news conference Thursday to announce new developments in the Phoenix suburb's efforts to retain the club.
The group said in a statement that the news conference concerns "new initiatives" regarding their January memorandum of understanding on a new training complex for the National League baseball club.
Mayor Scott Smith said in late May that the city had discovered ways to meet a July deadline to keep the Cubs despite the Arizona Legislature's rejection of proposed legislation.
Mesa is trying to keep the Cubs from relocating to Florida.
The decision comes at a time of political division between Chicago and Arizona.
Chicago's City Council and the Cook County Board both took measures to admonish Arizona for its controversial immigration law.
Protests have already taken place outside Wrigley Field when the Arizona Diamondbacks were in town.