Receiver Chad Ochocinco has been lobbying for the Bengals to sign Owens since the end of last season, when the Bengals' passing game lacked a deep threat.
"There's always been the speculation and perception out there [about coming to Cincinnati] and Chad kick-started it and lobbied to have me here as a teammate and I welcome it with open arms," Owens said, according to the Cincinnati Enquirer.
The newspaper reported that Owens had dinner with the coaching staff Tuesday night and would visit the Bengals offices on Wednesday.
Owens told WKRC-TV in Cincinnati that he would welcome playing with Bengals quarterback Carson Palmer.
The 36-year-old had tweeted earlier in the day that he was on his way to Cincinnati from Los Angeles.
"En route [at] Natti land!!" Owens tweeted. "i'll let u guys know how the mtg went! Cn't go 2 bad considering the pursuit of tht Lombardi shiny thing!!"
The Bengals went 10-6 and won the AFC North last season by relying on their defense and their running game. They lost to the New York Jets in their first playoff game since 2005, struggling to move the ball.
Cincinnati needs at least one proven receiver after releasing Laveranues Coles, who lasted only one season with the Bengals. Receiver Matt Jones, who was out of the NFL last season after Jacksonville released him for off-field problems, has signed a one-year deal with the Bengals.
It's unclear whether they have much interest in Owens, whose production declined each of the last two seasons with Dallas and Buffalo. Former Tampa Bay receiver Antonio Bryant was in Cincinnati on Tuesday.
Owens, a six-time Pro Bowl receiver, had 69 catches for 1,052 yards and 10 touchdowns with Dallas in 2008, and dropped off to 55 catches for 829 yards with five touchdowns last season in Buffalo.
Owens and Ochocinco are represented by agent Drew Rosenhaus, who didn't return a phone message Tuesday. Rosenhaus told Sirius NFL Radio on Friday night that he had talked to the Bengals about Owens, but wasn't sure where the team was headed.
Ochocinco tweeted on Tuesday night that he is ready for Owens to join the Bengals.
"Man it dont take that damn long to sign on the dotted line, lets go damit!!! You can be Batman i will be Robin, lets go!!" he said.
Bryant had career highs with 83 catches for 1,248 yards and seven touchdowns in 2008 with Tampa Bay. He needed surgery for torn cartilage in his left knee during training camp last year, and was bothered by pain in the knee all season. He finished with 39 catches for 600 yards and four touchdowns.
Cincinnati's passing offense finished 26th in the league last season even though Palmer was back from an elbow injury. The Bengals didn't have a reliable third-down receiver -- T.J. Houshmandzadeh left as a free agent for Seattle before last season -- and Coles failed to blend into the offense.
The Bengals also lacked a deep threat after Chris Henry got hurt. Henry later died in a fall from a truck during a domestic dispute.
Getting a receiver and a tight end are among the team's top priorities in free agency and the draft.
Information from The Associated Press was used in this report.