Unai Emery has been urged to sell the Armenian before the end of the European transfer window by ex-England international Winterburn.
Mkhitaryan has struggled for consistent game time at the Emirates since joining Arsenal as part of a swap deal which saw Alexis Sanchez move to Manchester United.
The forward did start Arsenal’s last game against Newcastle, a 1-0 win, but he was far from impressive.
In an inexperienced side which included two teenagers – Reiss Nelson and Joe Willock – Mkhitaryan made numerous errors and lacked a clear end product.
With youngsters like Nelson and Willock impressing in the first team, new signing Nicolas Pepe waiting in the wings and Alexandre Lacazette back to full fitness, Mkhitaryan could struggle to get regular minutes.
As a result, Winterburn believes Arsenal should look to offload the winger.
“Arsenal should look to sell Mkhitaryan to a European team this transfer window,” Winterburn told sportingbet.
“When everyone is back fit for Arsenal, Mkhitaryan is going to struggle to get any game time at all during the season.
“Mkhitaryan looks a frustrated figure, nothing seems to be working out for him on the pitch – his passes are misplaced, his shooting is off and he can’t beat his man.
“His performance against Newcastle on the opening game of the season wasn’t good enough, especially when you’re playing at the highest level.
“No doubt, Mkhitaryan is a talented player but he’s going to struggle to hold down a regular position when everybody’s fit.”
Winterburn also claimed Pierre-Emerick Aubameyang will be Arsenal’s “most important” player this season, after the forward notched the winning goal against Newcastle.
“Without a shadow of a doubt, Aubameyang will be Arsenal’s most important player this season,” Winterburn said. “You saw from the Newcastle game, he had very few opportunities to score but the one real opportunity that he got, his composure and finishing was perfect.
“If he stays fit, he’s going to have a huge season again for Arsenal, and will certainly be challenging for the Golden Boot again.
“It gives the team a huge lift when you know you’ve got a goal-scorer in your team. He is similar to Ian Wright in that sense.
“As a team, we knew that if you can keep a clean sheet, then Wrighty will usually pop up with a goal. Aubameyang is looking like that at the moment for this current side, which is great for the club.”