The France international has been with the Blues for the last two seasons, but he is expected to head for the exit door pretty soon.
The attacker has fallen out-of-favour under manager Enzo Maresca, and he would prefer a new challenge away from the Blues.
Hawkins claim that Arsenal were interested in signing the former Leipzig man in January and they are expected to return for his services.
Nkunku has looked a lost figure during his time with the Blues and it would be a surprise if Arsenal pursue his signature this summer.
However, a move can't be ruled out, considering the club have signed Kai Havertz and Raheem Sterling from the Blues in recent years.
Havertz has been a good signing from the west London giants, but Sterling has been a huge disappointment during his season-long loan stint.