The frenzy of speculation appeared to affect Hasselbaink - but he has looked back to his best lately and scored in last weekend's 3-0 success at Manchester City and yesterday's 2-0 victory against West Brom at Stamford Bridge.
Ranieri said: "Jimmy is a goalscoring animal. Look at him now and he's another person. He's scoring and wants to score more.
"He had a problem at the beginning of the season with his injury.
"So it was very important for Jimmy to break the ice against Manchester City - and he took a lot of confidence from that.
"Gianfranco Zola's our top scorer now, but I want to see the situation at the end of the season."
Hasselbaink's cool finish and Graeme Le Saux's 11th league goal in his 14-year career polished off the Baggies yesterday. 
Lampard admitted Hasselbaink was affected by Barcelona's interest, saying: "If a lot of people are talking about a move, it is unsettling.
"Jimmy's only human and maybe that did affect him a little bit. I think his confidence might have dropped a bit, and he gets frustrated if he's not quite firing.
"But you could see from the way he approached his goal against Man City last week that he was confident.
"That was the old Jimmy from last season - and for him to score again yesterday was great."
Lampard knows Hasselbaink's goals will be crucial in Chelsea's pursuit of a Champions League place.
"We need him scoring - and he's done that two games on the trot now, like last year when he was scoring in virtually every game," he added.
"It shows how successful he's been in his career that, when he doesn't score a for a few games, people start to wonder about him.
"Now he's shown what he's all about. And it's a big bonus when you've got someone like that up front who's confident and banging them in.
"He's always hungry, and that's a good goalscorer for you. He's a big character - and if you were a weak character, he'd walk all over you."
While Chelsea soared up to third, Gary Megson's men dropped back into the relegation zone. 
The Baggies boss acclaimed Zola, who starred again yesterday.
"Zola's one of everyone's favourite players. It's not just his goals - he's brainy, sharp and still quick at his age.
"He caused us problems playing one-touch football and he's an absolute credit.
"I really hope that, if he doesn't win Footballer of the Year, somebody like him does. He's an honest pro and a fantastic, hard-working player.
"He must have squillions of pounds in the bank, yet he runs about as if he's just happy to play football.
"He could retire and sit on a beach, but his performances this season have been magnificent."