While the Bengals do not comment on contracts until they are signed, they posted a story on their Web site that quotes Rosenhaus.
Rosenhaus said Lewis and defensive coordinator Leslie Frazier made "an impressive pitch" to Clemons, who would become the third free agent down linemen to join the new regime.
Since naming Lewis coach, Cincinnati has signed John Thornton away from Tennessee and Carl Powell from Washington. The team also has added linebacker Kevin Hardy and cornerback Tory James.
The 6-5, 280-pound Clemons turns 29 in 11 days. He had two sacks last season and has 35 for his career since Minnesota took him in the first round of the 1996 draft.