That is according to pundit and former Arsenal star Martin Keown.
The French boss and his Chilean midfielder appeared to avoid each other on the training pitch yesterday.
Wenger was approached by Sanchez, Mesut Ozil and Nacho Monreal.
Upon shaking the hands of the latter two, Wenger looked at Sanchez before turning back away without offering a handshake.
However, Keown believes the issue should not be blown up into a major problem.
"I think it is a lot of fuss over nothing," he told the Daily Mail.
"The players will have been at the ground an hour before going out on to the pitch and Arsene Wenger had probably seen Sanchez already and shaken his hand in the building.
"I do not see any problem at all."
It would come as no surprise if Sanchez and Wenger were not seeing eye to eye at present after the forward announced his desire to join Manchester City in the summer.
The 29-year-old was close to joining Pep Guardiola's side on deadline day before the move fell through.
Sanchez's contract at the Emirates expires at the end of the season and it is looking increasingly likely to he will leave the club either in January or on a free next summer.
Arsenal take on strugglers Everton this weekend, as they look for a first away win in the Premier League since last season.
