The Gunners dropped out of the Champions League places last season and no longer have that bargaining chip in discussions with the two players running down their current deals.
Arsene Wenger’s side have, however, progressed to the round of 32 in their current continental quest, with Swedish minnows Ostersunds awaiting them at that stage.
Arsenal are expected to mount a serious challenge for the crown, despite having made sweeping changes to their side in the tournament so far, but Smith doubts that even a repeat of Manchester United’s triumph from 2016-17 would be enough to get Sanchez and Ozil to pen fresh terms.
“I do not think it would persuade them to stay if they won the Europa League,” the former Gunners striker told Sky Sports.
“Jose Mourinho at one stage in the season went ‘I’ll put all my eggs in one basket’, and it paid off.
“That’s not always going to be the case.
“I think for Arsene Wenger he could go both ways.
“He is playing a totally different 11 in the Europa League anyway, it’s not like he’s mixing and matching.
“I think he will go that way for as long as possible.
“I think if they are in seventh position with no chance of getting into the Champions League spots then yes, he will probably do that [play his strongest side] in the latter stages, if they are still there.”
A top-four challenge in the Premier League remains Arsenal’s main focus at present, with the Gunners currently sat fifth in the table – one point back on Liverpool in the final Champions League spot.
They have also made it through to the quarter-finals of the Carabao Cup and will start another FA Cup campaign in January, so will need to decide where their priorities lie when it comes to knockout competition – domestic challenges or a European trophy hunt.