Barring one error in failing to keep out a long range Kyle Lafferty strike in the recent 4-1 defeat at Kilmarnock, former Livingston keeper Kelly has been excellent for the Steelmen since arriving in January, including saving a penalty in Saturday’s vital 1-0 home league win over St Mirren.
Boss Alexander said: “We’ve spoken to Liam and QPR about it after he said he would be interested in coming back next year.
“It has been on the backburner as we have tried to get permanent players signed up. But if his future lies out of QPR then we would certainly be interested.
“He has done great for us. In the last league game he made a mistake and I think he is still whipping himself about that.
“But he made a massive save from the penalty and he doesn’t have to make anything up to me as he has been fantastic since he came in. And we would really like to keep him.”
Encouragingly for Alexander, Kelly seems keen to remain in Lanarkshire.
"You want to be somewhere where you're appreciated and Motherwell feels like home for me," Kelly said. “I’m a Glasgow boy and it’s 20 minutes away from here. It’s perfect and I’m loving it.
“I would (like another crack at England) but you want to play somewhere that you’re wanted and you don’t want to force yourself on people.
"It’s still so unknown (the future) and it’s on QPR’s terms because I’m their player for the next two years anyway.”
Motherwell return to action this Friday evening (KO 7pm) in a home Scottish Cup fourth round clash against Morton. The game has been moved from Saturday due to Prince Philip’s funeral.
If the Steelmen come through this tie, they will travel to face either Stranraer or Hibernian in a quarter-final to be played on the weekend of April 24 and 25.