Sanchez, who has less than 12 months left on his deal at the Emirates, has been heavily linked with a move away from north London throughout the summer, with Bayern Munich, PSG and Manchester City all earmarked as possible destinations.
However, Wenger has quashed speculation over the Chilean's future, even though Sanchez has made no secret of his desire to play in the Champions League, a competition Arsenal will be absent from for the first time in two decades this season.
According to the Telegraph, PSG had considered making a move for Sanchez and were confident of succeeding before they completed the stunning signing of former Barcelona striker Neymar, who moved to the French capital for a world record £198m(€222m, $257m).
However, the report adds, the Ligue 1 outfit will no longer look to sign the Sanchez, as sources within the club categorically dismissed reports coming from the Chilean press, which suggested PSG were ready to table an £80m offer.
Earlier this summer, Bayern had ruled themselves out of the race for the 28-year-old because of his wage demands and Sanchez's representatives are now aware City look to be the front runners for the Arsenal forward, who scored 30 goals in all competitions last season.
However, Pep Guardiola could be prepared to wait until next season and sign the Chilean on a free, rather than open negotiations with Arsenal this summer, particularly as City have already spent in excess of £200m in the transfer window so far.
While it remains unlikely that Sanchez will sign a new deal with Arsenal, retaining his services for another 12 months would be a major boost for Wenger, as the Frenchman looks to secure a first Premier League title since 2004.
Keeping the Chile international, who scored 30 goals in all competitions last season, would also allow Wenger more time to bed in record signing Alexandre Lacazette, who arrived earlier this summer from Lyon in a £52.6m deal.