Scharner, who has been with the Latics for just over four years, is out of contract this summer, with Fulham and Stoke both linked with the 30-year-old midfielder.
The Austrian hardly did himself any favours with his behaviour on Wednesday during the goalless home draw with Portsmouth.
Scharner was seen arguing with team-mates as they left the pitch at half-time, and following his substitution just before the hour mark, marched straight down the tunnel and apparently off home before the game ended.
Martinez, though, has not ruled out the possibility of the player remaining at the DW Stadium, but any talks will have to wait until after the season when Wigan will hope to have secured their top-flight status.
"We're in a position where we need to stay in the Premier League, and that's our aim," said Martinez.
"There are six clubs fighting to avoid the remaining two relegation places, and that's not going to change until late in the campaign.
"We need to sort that out first, which is our priority, and then at the end of the season we will sit down and see how Paul is feeling, and we'll make a decision.
"Paul has been here long enough, he knows the club well enough, and I'm sure he'll have the right feeling to determine his future."
As for Wednesday's tantrum, Martinez looks set to let the matter rest, although it remains to be seen what part Scharner will play in tomorrow's clash with Arsenal at the DW Stadium.
"Paul has been through everything in football. He is an experienced player," added Martinez.
"We were all frustrated with what happened on Wednesday, even more so when you look at the stats - we had 24 attempts on goal - and you don't get a result.
"With Paul, he wasn't happy with himself, with the performance, the result, with being substituted. It was a mixture of emotions.
"But everything was controlled in the right manner. There was nothing disrespectful.
"I know Paul inside out, and if there is an issue we will deal with it behind the scenes, but in this situation I don't see anything away from a normal reaction."
Martinez is again likely to be without Hendry Thomas for the visit of the Gunners due to a quad injury, while defender Gary Caldwell completes a three-match ban.
Wigan are aiming for their first league win over Arsenal after a run of eight defeats and a draw since they were promoted to the top division.
"Everybody will expect Arsenal to win, so we have to make sure we are on top of our game," said Martinez.
"After already beating Chelsea and Liverpool at home this season, we have to again show that on our day we are capable of beating anyone."