The 20-year old joined the Brum from Manchester United on an initial one-month loan deal last week before scoring all four goals in a dream debut in their 4-1 victory over Sheffield Wednesday on the weekend.
Clark is aware he may only have the attacking midfielder until mid-October but insists he would like to keep him longer if it were possible.
"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."