According to the Sun, the New York Rangers, Detroit Red Wings, Toronto Maple Leafs and Boston Bruins all have interest in Smyth.
Smyth, 35, is in the final year of his contract and can become an unrestricted free agent July 1.
In 55 games with the Oilers so far this season, Smyth has registered 16 goals and 20 assists for 36 points, tying him with Sam Gagner for third on the team in scoring.
Meanwhile, the Sun also reports Andy Sutton's agent, Pat Morris, was in Ottawa Saturday to see if he could get a one-year contract extension done with the Oilers.
Sutton, 36, can also become a UFA this summer. He's already being dangled as trade bait and could be dealt by the deadline if a new contract isn't reached.
More Trade Deadline Info
List of Trades
| No-Trade/No-Movement Clauses
| Top 25 Available Players
| Team-by-Team Cap Info