Although Olivier Giroud signed a new deal with Arsenal, Arsene Wenger is keen to beef up his attack.
Meanwhile, the Blues have been tracking Spanish striker Morata, and recent claims have suggested Conte is open to a swap deal involving Thibaut Courtois.
Alvaro Morata is the subject of strong interest from Premier League clubs
Olivier Giroud only recently signed a new deal with Arsenal
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Express Sport brings you 10 key stats from Arsenal's win over Burnley
But according to the London Evening Standard, a deal for either side could depend on whether or not Benzema stays at the Bernabeu.
The report suggests the 29-year-old has interest from China.
If Benzema leaves, it is unlikely Zinedine Zidane would wish to let Morata head for the exit too.
Karim Benzema's Real Madrid future remains uncertain
Chelsea are thought to be eyeing Morata as a replacement for Diego Costa, who could still leave the club come the summer.
Costa was involved in a bust-up with the fitness coach on the eve of the 3-0 win over Leicester.
However, he returned to the starting line-up last Sunday and scored in his side’s 2-0 victory against Hull.