The Elland Road club have an option to secure the 6ft 5in defender for £3million once he has made his 20th appearance.
And Whelan believes the Swede would be a bargain buy for the Championship club.
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Pontus Jansson is currently on loan at Leeds United
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Jansson (left) played for Sweden against France during the international break
£3m these days is next to nothing
Noel Whelan
“I think everything needs to be put in place now,” Whelan told the Yorkshire Evening Post.
“We need to be talking to him and we need to be sorting out contracts.
“The fans love him and the players have benefited from him being in the side so I think the club needs to put their hand in their pocket pretty deep and get this one signed up.
“£3m these days is not a lot of money and you are getting a lot of player for that."
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Noel Whelan started his career at Leeds before being sold to Coventry for £2m in 1995
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Garry Monk's Leeds side face Newcastle on Sunday
Jansson joined Leeds in the summer and has made 13 appearances for the club already.
The 25-year-old scored in the 3-2 win at Norwich earlier this month and played twice for Sweden during the recent international break.
Leeds manager Garry Monk was handed funds to buy players in the summer, with forwards Marcus Antonsson and Kemar Roofe arriving for a combined £5m.
And Whelan is sure the club can afford to secure Jansson's signature on a permanent deal.
“You have got to put it into perspective and £3m these days is next to nothing – it’s a drop in the ocean but what you are getting is very, very good player so in the long term £3m is a very good business deal for what you are getting," he said.