Cleveland owns the No. 12 and No. 19 pick in the upcoming draft, the latter of which came via the Buffalo Bills.
A source from the Titans told ESPN's Paul Kuharsky that the Browns have not made an offer for the No. 2 pick and a source close to the Browns told Kuharsky that there have not been substantive talks with Tennessee.
Last year, the Browns drafted quarterback Johnny Manziel in the first round with the No. 22 pick. Manziel started two games last season and checked into a rehab facility in January. He was released earlier this month.
Browns coach Mike Pettine recently told reporters that Manziel is "very much in our plans" and that Cleveland has not yet built a depth chart for its quarterbacks. Cleveland signed 12-year veteran quarterback Josh McCown in February.
Mariota, the 2014 Heisman Trophy winner,won't be attending the draft in Chicago and told the NFL it is important to him, personally and culturally, to be in Hawaii to celebrate the next step in his life.
The 2015 NFL draft begins on Thursday.
- Molly Geary