Cole, who joined last October after leaving Doncaster Rovers, is out of contract this summer but he would clearly be an asset going forward having scored 10 goals in 25 games for Motherwell this season.
Alexander said: “We spoke to him quite a while ago about a contract and it’s still ongoing. But we would be delighted to keep him. I think we can help him improve and get to the next level.
“I think he needs a consistency of being at one club for a certain amount of time. He has led a little bit of a nomadic existence up to now but he certainly has the qualities of having a top-level career and I believe we can help him with that, but we will see how it goes. He’s been excellent.
“You can’t ask any more of a number nine. His goals stand out for themselves, they are there for everyone to see, but his all-round contribution and link-up play and defensive side has been excellent.
"As it has been with the others, we can’t win games with one centre forward and a defender, it has to be a whole team performance.”
Motherwell were boosted on Saturday by the inclusion of incomers Jake Hastie and Sam Foley from the start, with both having fine matches.
"It was an opportunity to reward them for how they've trained,” Alexander said.
"Sam, that’s his first game for a long time. But the way he trains, he keeps himself in top form and Jake Hastie’s been putting in the extra work behind the scenes to get back in the team and I thought he was a real threat."