Lucroy, 30, must first approve the deal because of his limited no-trade clause that allows him to block trades to eight teams, including the Indians.
The clubs reportedly are in the process of exchanging medicals.
A two-time All-Star, Lucroy is batting .300 with 13 homers and 50 RBIs this season. He has a $4 million salary this year as part of a contract that includes a $5.25 million team option for 2017. It's possible that Lucroy could be asking the Indians for an extension on his current deal or to increase the value of his option for next season.
According to reports, the Brewers would receive four minor league prospects from the Indians if Lucroy signs off on the trade. Included among the prospects are prized switch-hitting catcher Francisco Mejia, 20, and outfielder Greg Allen, 23.
Shortstop Yu-Cheng Chang, 20, would also be headed to Milwaukee, along with another prospect.
Mejia, Cleveland's No. 6-ranked prospect renowned for his arm strength, is currently on a 42-game hitting streak with Class-A Lynchburg. During that span, he is batting .385/.408/.609 with eight home runs and 37 RBIs.
Lucroy was held out of Saturday night's 5-3 win over the Pittsburgh Pirates as Milwaukee considered trade possibilities. The New York Mets and Texas Rangers were among the teams linked to Lucroy, with New York reportedly offering a three-player package that included the club's own catcher, Travis d'Arnaud, along with a top prospect and one more piece.
The Indians have been in the market for a catcher since Yan Gomes was put on the disabled list on July 18 with a shoulder injury. Gomes, who struggled most of the first half of the season, is expected to miss four to eight weeks.
With Gomes out, Chris Gimenez and Roberto Perez have been sharing catching duties, but neither has been productive. Gimenez entered Saturday's game batting .200, and Perez -- who missed six weeks with a broken thumb -- is in a 1-for-23 slump.
Lucroy has spent his entire career with the Brewers, who selected him in the third round of the 2007 draft at No. 101 overall. He made his major league debut in May 2010, recording a hit in his first at-bat.
Information from ESPN's Jerry Crasnick and The Associated Press was used in this report.