Manchester United have struggled for goals all season and there are growing doubts over the future of leading scorer Zlatan Ibrahimovic, who is out of contract this summer.
The Red Devils have been linked with a host of forwards, most notably Atletico Madrid's Antoine Griezmann, but Express Sport understands that interest has now cooled.
And having watched his former club squander chances all season, Robson is convinced Arsenal's Sanchez is the perfect fit at Old Trafford.
Sanchez was Arsenal's player of the season, top scorer and man of the match in the FA Cup final win over Chelsea, but has just 12 months remaining on his Gunners contract.
Bryan Robson wants Arsenal's Alexis Sanchez at Manchester United
The Chile international is no closer to penning a new deal at the Emirates and has been heavily linked with a move away this summer.
"(Sanchez) has played at a club like Arsenal, so he can handle the pressure, that's 100 per cent guaranteed," Robson said.
"His character is right, he's a tough player, he's really skilful, he works hard for the team, he can score and he create goals.
"When you put that package together, he is the type we would like here.
Jose Mourinho in market for goalscorers this summer Alexis Sanchez and Per Mertesacker's hilarious interview Sun, May 28, 2017
Click for the best snaps and reactions to Alexis Sanchez and Per Mertesacker's hilarious post-FA Cup final interview
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Per Mertesacker was a towering presence during his post-match interview…
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"Whether we can achieve that or Mourinho thinks the same… people always have different opinions on players."
Sanchez joined Arsenal from Barcelona in 2014 and has gone on to score 72 goals and provide 42 assists in 144 appearances, winning two FA Cups in the process.
But after Arsenal failed to qualify for next season's Champions League, Sanchez may be tempted by a switch to Europa League champions United.