However, Cueto's agent said his client is in no hurry to sign a contract and he would not be surprised if the right-hander hasn't picked a team by Thursday, when the MLB winter meetings conclude in Nashville, Tennessee.
"I don't expect anything," Cueto's agent, Bryce Dixon, told ESPNdeportes.com on Saturday. "I don't have a specific timetable. It may occur during or after the winter meetings. We are in no hurry.
"We have some offers and we will have several meetings in Nashville, but right now I could not tell if Cueto will have a team after the conclusion of the meetings. We have plenty of time until the beginning of the season."
Cueto, who will turn 30 in February, was one of the best free-agent pitchers entering the offseason and now is the only ace left on the market.
Price went to the Boston Red Sox for a reported seven-year, $217 million contract. Greinke (six-year, $206 million deal with the Arizona Diamondbacks), Zimmermann (five-year, $110 million deal with the Detroit Tigers) and Samardzija (five-year, $90 million deal with the San Francisco Giants) also have agreed to deals.
Cueto turned down a reported six-year, $120 million offer from the Diamondbacks last month, prompting the NL West team to focus, and ultimately agree, on a deal with Greinke.
"It was a low offer for the market," Dixon said. "We didn't have to think hard to reject that offer. Arizona wanted to do something fast, but we didn't want to take something below market value for a No. 1 starter, and with the recent events, I think that time gave us the reason."
Cueto went 11-13 with a 3.44 ERA between the Cincinnati Reds and Kansas City Royals in 2015. It was a subpar season by his standards, but he did help the Royals win their second World Series in franchise history.
In his eight-year major league career, the Dominican Republic native is 96-70 with a 3.30 ERA. He has averaged 214 innings per 162 games.
"Johnny is in San Pedro de Macoris [Dominican Republic] waiting for the best offer," Dixon said. "I can almost guarantee that the team that finally takes Cueto will be very happy for the duration of the contract."