The Browns, according to the source, made an offer to the Titans that includes the team's two first-round picks -- 12th and 19th overall.
Both teams privately denied the report. A source with the Titans told ESPN's Paul Kuharsky that the Browns had not made an offer for the No. 2 overall pick, and another source close to the Browns said there have been no substantive talks with the Titans -- claiming these discussions commonly take place as the draft approaches. ESPN's initial source, however, said the talks were more substantive than that.
Meanwhile, a league source told ESPN NFL Insider Adam Schefter that the Titans have gotten calls from multiple teams inquiring about what it will take to trade for the second overall pick.
The NFL draft begins Thursday night in Chicago.
Browns general manager Ray Farmer addressed Mariota and trades in general last week.
"I would go up if it was the right circumstance, and I would go back if it was the right circumstance," Farmer said.
He added any trades usually happen on draft night.
"A lot of the scuttlebutt that you hear and the conjecture and the noise that's out there, it changes the complexion of trying to get a deal done," Farmer said. "If everybody thinks that you want something, your price just went up."
The Browns drafted Johnny Manziel in the first round last year, and while the team has said it believes Manziel can be an effective NFL starter after his stay in rehab, it also has said it would pursue every possibility about improving at the quarterback spot.
The Browns also signed Josh McCown as a free agent in the offseason.
The starting point for any possible trade would be the Browns' two No. 1 picks. What the Titans might want in addition to those picks isn't known.
When Washington traded up for Robert Griffin III in 2012, the Redskins swapped first-round picks with the St. Louis Rams and also sent two more first-round selections and a second-rounder to the Rams.
Mariota, who won the Heisman Trophy last season, is considered the second-best quarterback in the draft behind Florida State's Jameis Winston. Mariota threw for 105 touchdowns and 14 interceptions in 41 starts at Oregon.
"We'll continue to address the quarterback," Browns owner Jimmy Haslam said in March at the NFL owners meetings, "until we get the kind of quarterback that can help us be a consistent winner."
ESPN Titans reporter Paul Kuharsky contributed to this report.
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