Former Reading winger Convey, who joined the Reds from Sporting Kansas City in May this year, is likely to be offered a reduced salary while ex-Cardiff City, West Bromwich Albion and Norwich City striker Earnshaw may also need to take a cut according to Bezbatchenko.
"We're talking to Bobby's agent," he told the Toronto Sun.
"He served us well and had a great year this year in terms of number of games played. He wasn't injured so I think there could be something there.
"It could go either way."
On Welshman Earnshaw, who arrived from Cardiff in February, the TFC GM added: "He's a good guy in the locker room. He's respected worldwide. We're in talks to bring him back at (a contract figure) that would be agreeable to both us and Earnshaw."
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