City Engineer Beth Huning said an escalation of progress on the site is expected at the end of the year and the construction will be completed by next October or November.
"There's a lot of things going on all over that site right now," Huning said.
A park-bond package was approved by voters in November to turn Mesa's Riverview Park into a "signature park," with space for the Cubs as well as public events, play areas and other amenities, The (Phoenix) Arizona Republic reported Thursday.
The price tag for the construction and the remodeling of the Cubs' existing spring training site, Hohokam Park, will exceed $120 million, the city manager's office said.
The city is negotiating a deal with the Oakland A's to move their spring training from Phoenix to Hohokam Park, the newspaper said.
City Manager Chris Brady said public spending on the Cubs' facility is capped at $84 million. The team will pay any bills beyond that figure.
The look of the new stadium is still under development, Huning said, but the city recently released an artist's rendering that included an upper deck shading the field and an old-fashioned feel reminiscent of the Cubs' Chicago home in Wrigley Field.