The Netherlands international has been a mainstay in the Nerazzurri squad since 2009. In that period, he helped the club win the European Treble in his debut season and the Coppa Italia the season after.
But he also had to endure a trophyless season last term during which he also played poorly, fuelling rumours that he could consider a departure from the club in the summer transfer window.
The playmaker has seen six managers during his brief Inter career but new coach Stramaccioni, who values the player highly, stated that he would not be averse to selling the Dutch player. But he also said that he would not do it on the cheap and unless a bumper offer came in, he warned the ex-Real Madrid midfielder to turn his focus towards preparing for the new campaign and help the side improve upon last season's sixth-placed finish.
"As far as I know, [Sneijder] is an Inter player and will remain. I have not had any other news from the directors, the club, or the player himself," Stramaccioni revealed in an interview with Sky.
"Though, of course, if an offer arrived like the one that attracted Zlatan Ibrahimovic and Thiago Silva, anyone could be sold, except for Ivan Cordoba and Javier Zanetti."
Club captain Zanetti, 38, will be starting his 18th season with the Serie A giants while his deputy Cordoba has already declared that the coming season would be his last at the club.
Inter centre-back Walter Samuel also gave a message of solidarity ahead of the new campaign, calling on his team-mates to play without any added pressure in order to bounce back from a disappointing season that saw them suffer 14 defeats in the league.
"We must be ourselves," Samuel declared.
"There have been a few changes in the squad, and now there are many young players.
"We, on our part, look to help them and each other to win the Scudetto, Coppa Italia, and the Europa League.
"Are we too busy? We've always been busy. Now we have a new group but that must not change."
Inter won their latest pre-season friendly against Slovenian side Koper with goals scored by Samuel and Coutinho. They will next participate in the TIM friendly tournament alongside Serie A rivals Juventus and Milan.
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