Niners owner Jed York is in Cincinnati to interview Jackson and NFL Media's Ian Rapoport reported the team could hire Jackson as soon as Sunday.
Despite a report that Jackson is the frontrunner for the 49ers' job, it is not a foregone conclusion he is headed to San Francisco, a source told Cleveland.com.
Jackson, the former head coach of the Oakland Raiders, will go into interviews Sunday with the Browns and 49ers with an open mind, and he is equally interested in both jobs, the source told Cleveland.com.
Jackson is available to be hired now after the Bengals lost a heartbreaker to the Pittsburgh Steelers 18-16 in the AFC wild-card game Saturday night.
The 49ers have considered other candidates, including Buffalo Bills assistant head coach Anthony Lynn, Browns offensive coordinator John DeFilippo, Tampa Bay Buccaneers offensive coordinator Dirk Koetter and former Philadelphia Eagles head coach Chip Kelly.
The Browns also plan to interview Carolina Panthers defensive coordinator Sean McDermott on Sunday. The Browns interviewed New England Patriots defensive coordinator Matt Patricia on Saturday. The Browns also have interviewed Detroit Lions defensive coordinator Teryl Austin and former Bills head coach Doug Marrone, now the Jacksonville Jaguars' offensive line coach.