The Manchester United youngster scored four goals on his debut, but with his current contract set to expire after one month the manager is hoping to keep him for longer
Lingard, who is on a one-month loan at St Andrews, enjoyed an incredible debut as he scored all four goals to help the Midlands club beat Sheffield Wednesday 4-1 on Saturday
And Clark is keen to extend the deal so that Lingard can continue helping the club move up the table from their current position of 18th.
"What we have got to try and do is continue to win games and for Jesse to enjoy his football to make the stay longer," Clark told the Birmingham Mail.
"That's what we aim to do because, you know, we certainly don't want him here just for the short term. We want him here for as long as possible.
"The month will be up quite quickly. Manchester United need to see that he is developing as a player and is enjoying the environment where he is playing."
Clark also confirmed he had been in contact with United manager David Moyes regarding Lingard's performance.
"I sent a text to David Moyes after the game Saturday," he continued. "I see by the television footage that he was at the Hawthorns.
"He just replied saying he was delighted for the lad."