The 23-goal attacker has been included on the club’s retained list, which was published on Wednesday.
Conn-Clarke not only won a place in the National League Team of the Season but also plaudits a plenty - and the Parkinson is realistic about what happens next.
Alty fell at the play-off semi-final hurdle, defeated at eventual Promotion Final winners Bromley.
According to the Sale & Altrincham Messenger, his exceptional form in an outstanding campaign has attracted mounting interest from clubs.
The Robins boss said that he would love Conn-Clarke to be wearing the red and white next season.
But Parkinson said: “I would love to reassure everyone that Chris will still be with us next season but, in all honesty, I can’t.
“When a player does what he has done, in terms of goals and assists, the bigger clubs are going to come calling, and it’s very difficult to stop that natural next step happening.
“If he is still with us at the start of next season, I will have the biggest smile on my face you have ever seen. If not, I won’t exactly be amazed.”