Hannah Scott has set up a website page which has raised hundreds of pounds already for Marie Curie Cancer Care, where Mr Jardine was treated for throat cancer before he died last month.
Writing on the JustGiving page, she said: "In his last months Marie Curie nurses did everything in their power to make my Grandad as comfortable as possible. It was thanks to them that he was able to stay at home when he was told that the cancer was terminal. I want to raise as much money as possible to give other families the same support.
"Any donations that you could give in his memory would be much appreciated." Ms Scott plans to take part in the jump on May 17.
More than 1000 mourners, including former Rangers and Manchester United managers Walter Smith and Sir Alex Ferguson, attended Mr Jardine's funeral in his home city of Edinburgh last week.
He made almost 800 appearances in his Ibrox career, helping the side secure three league championships, five Scottish Cups and five League Cups. He also played a pivotal role in the club's European Cup Winners' Cup win in 1972.