"I just live for today. I don't want to worry about what lies ahead," Smyth told the Edmonton Journal. "You just want to compete right now and, right now, we've got a so-called young team and a lot of the players haven't played in the playoffs.
"I'm sitting here today worrying about today."
Smyth, who turned 38 on Friday, is also set to become an unrestricted free agent July 1. He's unlikely to sign a new deal with the Oilers, which furthers speculation that a trade is on the horizon.
"I just want to be an asset as much as I can," he said. "Right now, I'm positioned in the middle and you try to relish the opportunity as best you can. You've got to fight for another contract and it's just a matter of just playing as hard as you can and playing the right way."
In addition to Smyth, Oilers right wing Ales Hemsky is expected to be moved by the trade deadline.
Hemsky, 30, has been shopped for the past few years, but the Oilers have elected to keep him.
During the off-season, the Oilers tried to trade him, but didn't find a deal they liked. Hemsky said earlier in the season he still expects to be moved.