His contract expires at the end of the campaign and Pellegrini has challenged the England international to prove himself worthy of an extension.
"When you need to renew your contract, of course you must demonstrate why you need to renew," said the Chilean.
"We know what Andy can give to our team, now he must demonstrate he is able to do it week by week.
"He has now the last six months, and I hope that he will be able to do it."
Pellegrini added: "For the moment, he can be a very important substitute.
"We know what he can give to our team, the other day in 15 minutes, he had two or three shots, headers.
"All the other defenders must be worried if they see Andy near the box, he can give a lot of important things to our team."