Mulder was originally slated to meet with Indians general manager Mark Shapiro on Friday, the paper reported, but the seven-year veteran is just returning from his honeymoon in Tahiti.
"Mark Shapiro does a great job selling what the Cleveland Indians have to offer," said Gregg Clifton. "I think he's in a good spot to get Mulder to come to Cleveland."
Despite the injury, which may cost him the first few months of next season, Mulder is possibly the top free agent pitcher still available, now that former teammate Barry Zito is San Francisco-bound.
The Indians have offered Mulder a two-year deal, according to the paper.
The 29-year-old hurler had the most disappointing year of his career in an injury-plagued 2006 season, going 6-7 with a 7.14 ERA in 17 starts for the World Series champion Cardinals before being shut down.
The two-time All-Star led the American League with 21 wins for Oakland in 2001, when he finished second to Roger Clemens for the AL Cy Young Award.