Bob Nightengale of USA Today reported the offer Wednesday and noted Hosmer, who spent the first seven seasons of his MLB career with the Royals before hitting free agency this offseason, also has a seven-year, $140 million proposal on the table from the Padres.
Hosmer is seeking an additional year or two, but it's unclear whether Kansas City or San Diego will increase their team-record offers, per Nightengale.
The 28-year-old infielder is coming off his most complete offensive season to date. He posted a .318/.385/.498 triple-slash line with 25 home runs and 31 doubles while playing all 162 regular-season games for the Royals in 2017.
In September, Hosmer said he wasn't sure how his free-agent foray would end but hoped Royals fans would remember him fondly if he landed elsewhere, per John Pepitone of WDAF.
"Just wanted to do everything the right way, on and off the field," he said. "[General manager] Dayton [Moore] and his staff put a lot into not only us being good baseball players, but good people off the field. Doing everything the right way, that's what everybody wants to be remembered as."
Hosmer's resume includes four Gold Glove Awards, a Silver Slugger Award and an All-Star Game MVP Award from the 2016 Midsummer Classic, which was held in San Diego.
He also helped Kansas City win its first World Series title since 1985 in 2015.