The pair have clashed bitterly over Heather Trott (Cheryl Fergison) in recent months, but the Walford favourite's tragic death could unite them in a future storyline.
As revealed yesterday, Andrew will be staying on Albert Square as show bosses want to keep him for at least another year.
Grover, discussing his character's future, told TV Times: "We'll see a lot more of what Andrew's about.
"He and Shirley could become friends. They've been through so much, and the one thing they've got in common is that they both loved Heather."
Andrew finds himself in the frame for Heather's murder in the coming days, with Shirley among those who suspect him of being guilty.
However, news that Andrew will be sticking around suggests that he won't be under police scrutiny for long.
EastEnders continues tonight (March 21) at 7.30pm on BBC One.
> EastEnders spoiler: Shirley is left devastated over Heather
> EastEnders spoiler: Andrew is suspected of killing Heather
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Watch Shirley's EastEnders character trail below: