The Premier League champions have been heavily linked with a move to sign the Spain international as a replacement for Diego Costa.
Chelsea were initially thought to be prioritising the signing of Everton striker Romelu Lukaku but the Belgium international completed a £75m switch to their bitter rivals Manchester United earlier this month.
The Blues have signed goalkeeper Willy Caballero, AS Roma defender Antonio Rudiger and Monaco midfielder Tiemoue Bakayoko in the summer transfer window so far.
However, Chelsea boss Antonio Conte has been unable to bolster his attacking options despite the lure of Champions League football at Stamford Bridge next season.
Morata was heavily linked with a move to Chelsea last summer but a deal failed to materialise as the 24-year-old returned to La Liga giants Real Madrid.
Former Arsenal striker Robson believes Morata would be a good addition to the Chelsea team ahead of the defence of their Premier League crown.
“When Morata played for Juventus, I thought he was absolutely outstanding,” Robson told ESPN FC on Monday.
“He led the line well. He can hold up the play, he can link up the play, he can run in behind and he can score goals.”
Chelsea won the title with two games to spare last season after finishing seven points ahead of closest rivals Tottenham Hotspur.
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