Northern Ireland international Lafferty scored an 11-minute first-half treble to secure a 3-0 win over Dundee United and boost Kilmarnock's chances of beating the drop.
Kilmarnock jumped out of the relegation play-off spot, moving two points clear of Ross County and five ahead of bottom club Hamilton with just three games remaining.
Lafferty has notched 10 goals since joining the club in February on a short-term deal and Wright is keen to keep him.
Wright said: "You know what he can do, he's a top player and he gives that extra quality at the top end of the pitch. He's enjoying his football and he plays well with a smile on his face.
"I've been really impressed and he's probably in the best run of goals for a long time.
"The end of the season? Apart from the fact he told everyone that if we stay up I'm buying him a bulldog. I'll be doing everything I can to keep him if we stay up.
"I'm sure once we get enough points we'll be sitting down with him.
"Am I buying him a dog? No chance. But I sense this could be a home for him. The relationship I've had with him makes me hopeful but I'm realistic if he keeps scoring other clubs with bigger budgets might come in for him."
Wright insists there is still work to be done to avoid relegation.
He said: "There are lots of positives and we've got ourselves in 10th place with the other results. We've played well to get into this position but there's still a lot of hard work.
"It's a big night because we've been in the bottom two for a long time and have been playing catch up. We've put ourselves in a strong position where it's in our hands but the job still isn't done."
Dundee United manager Micky Mellon made seven changes to the side which knocked Forfar out of the Scottish Cup and handed a debut to 16-year-old central defender Kerr Smith.
And Mellon insists it is important to give youngsters a chance.
Mellon said: "People bang on about youth all the time but when they come in they have to deliver and give the team the opportunity to gain results.
"I'm pleased with our young players. We don't put them in as a favour, we believe they're ready to have a blast at it.
"When the opportunities come we give them. If he's good enough he's old enough. Kerr's a brilliant young player who's been knocking on the door for some time."