The Northern Ireland international is out of the contract at the Banks's Stadium at the end of this season, but boss Dean Smith stated on Saturday that the Saddlers are in talks over a new deal with the 21-year-old striker.
It came after Grigg netted a brace to help see off Shrewsbury 3-1, adding to the hat-trick he bagged at Carlisle in midweek, taking his tally for the season to 16.
"It's where I've started my career and the gaffer has given me my chance so I would be happy to stay," Grigg told the Express & Star.
"I just want to concentrate, though, you never know where we're going to be at the end of the season so I'll concentrate on getting us into the play-offs and we'll go from there.
"I'm focusing on my football and we'll see what happens in the next few weeks."
Speaking after Saturday's victory over neighbours Shrewsbury, which left eighth-placed Walsall five points off the top six, Smith said: "He (Grigg) needs another season with us under his belt, and if he does that he can play where he wants.
"If clubs come in with an unbelievable offer you have to listen, but if he goes to a big club now he is not going to play and develop as he is with us. He needs to maintain his development."