Manziel, who has been widely projected as a high first-round pick in next month's NFL draft, also will visit with the Browns this week, according to the source.
Although they did not attend his pro day at Texas A&M, the Browns recently have been linked with Manziel, the former Heisman Trophy-winning quarterback who has emerged as one of the most polarizing prospects in this year's draft class.
Manziel recently was tabbed as the No. 4 overall pick to the Browns in ESPN NFL draft expert Mel Kiper's latest mock draft. Veteran Brian Hoyer, who is attempting to bounce back from a serious knee injury, is the only quarterback currently on Cleveland's roster.
Manziel also reportedly scored a 32 on the Wonderlic test at February's NFL scouting combine, potentially boosting his draft stock. The Wonderlic is a 50-question test administered to all combine participants that measures cognitive ability. A score of 20 is indicative of "average" intelligence and roughly equivalent to an IQ of 100.
The Browns went 4-12 last season and are rebuilding their roster under new general manager Ray Farmer and first-year coach Mike Pettine.