Arsenal had been linked strongly in recent days with a move for the centre-back, who was recently selected for France's 23-man World Cup squad.
Reschke, however, poured cold water on the rumours and appeared to confirm that Pavard's future is in Germany.
The sporting director said: "I am very relaxed about that. The statements he made are absolutely fine. That’s the manner in which we have held our talks. He had an exceptional season for VfB and it’s clear that he is in the focus on the international top clubs.
"We are in constant exchanges with Benji and his agent and we are well aware of what’s going on.
"In extending his contract, we naturally spoke about his career planning. We’ve discussed the national team, the Champions League and that it’s our mutual focus to have him play at VfB next season.
"We expect that to be the case – there have been no offers, no talks with other clubs and there’s no change to the situation."
Pavard rose to prominence in 2015 after coming through the ranks at Lille and has made a swift ascension up the football ladder, playing every minute of Stuttgart's Bundesliga campaign in 2017/18 and being called up for the national side in the process.
Reports in France suggested the Gunners were prepared to offer £44m for the defender's signature but it appears Reschke and Stuttgart have other ideas.