The person familiar spoke on condition of anonymity to The Associated Press on Friday because the deals are still pending physicals.
Gilbert is on Saskatchewan’s confidential 50-man negotiation list. The timing is coincidental since the Browns recently hired former Roughriders Head Coach/GM Chris Jones as a defensive assistant.
Burnett was released by Pittsburgh this week. The person said he could get a multiyear deal with Cleveland. Gilbert played for the Orlando Apollos of the defunct AAF. He was the league's passing leader with 2,152 yards.
The Browns have been looking for a safety since trading Jabrill Peppers to the Giants in the deal for star Odell Beckham. This week the Browns acquired safety Eric Murray in a trade with Kansas City.
Burnett's role was reduced last season with the Steelers after the team drafted Terrell Edmunds in the first round. The 30-year-old Burnett was also slowed by a groin injury and played in 11 games.
(With files from Associated Press)