The Chile international’s future has been a source of relentless debate so far this summer given the uncertainty surrounding his long-term plans.
Sanchez has less than 12 months remaining on his current Arsenal deal and hasn’t agreed an extension with the north London club.
The South American has been attracting interest from Arsenal’s Premier League rivals Manchester City in what would be a controversial summer move.
Sanchez worked with Manchester City boss Pep Guardiola during his spell at Barcelona before the Chile star moved to Arsenal in a £35m deal in 2014.
Arsenal signed Bosnian defender Sead Kolasinac from Schalke 04 in a free transfer last month before the Gunners recruited Alexandre Lacazette in a club-record £52m deal from Ligue 1 side Lyon.
Speaking to ESPN FC about whether Arsenal will finish in the top four next season, former Gunners striker Robson said:
“Based on the current squad, I think they can get into the top four and will do if they can keep Alexis Sanchez.”
Arsenal finished in fifth place in the Premier League table last season to miss out on a place in the Champions League this coming season.
The Gunners did win the FA Cup thanks to a 2-1 victory over Premier League champions Chelsea in the final.
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