Ospreys wing Williams won the prestigious award last season ahead of Wales skipper Ryan Jones and New Zealand fly-half Dan Carter.
And the 32-year-old Welshman believes British & Irish Lions team-mate O'Driscoll would be a worthy successor after he helped Ireland and Leinster clinch a Grand Slam and Heineken Cup double.
O'Driscoll has been nominated alongside seven other world stars, including Leinster colleague Jamie Heaslip, and Williams admits he would love to see the Ireland captain pick up the prestigious honour.
"It would be nice to see Brian win the award. He's a great friend of mine and he deserves to win it - let's hope it goes to him," said Williams.
"There's a couple of great players on the list. Matt Giteau has been the most consistent player this year but after everything he has achieved, I hope it will be Brian.
"He's won the Grand Slam, Heineken Cup, had a great tour with the Lions, although we were disappointed not to win the series, and he scored again at the weekend on his 100th Test cap.
"He's back to his best and he's worked so hard to get there. He fully deserves the accolade."
O'Driscoll has been shortlisted for rugby's top prize twice before - in 2001 where he was pipped by countryman Keith Wood and a year later in 2002.
As well as Australian fly-half Giteau, O'Driscoll faces stiff competition from South African pair Francois Steyn and Fourie du Preez and All Blacks captain Richie McCaw, as well as Lions back row pair Tom Croft and Heaslip.
But Lions and Wales coach Warren Gatland has also endorsed the 30-year-old's case, after O'Driscoll claimed the Six Nations Player of the Year title as well as being the top try-scorer in both in the Six Nations and Heineken Cup.
"Over the last 12 months, Brian has possibly played his best rugby for a number of years," claimed Gatland.
"It was great to be involved with him on the Lions tour because I coached him as a kid and gave him his first cap against Australia.
"He is now a world-class player and it was great to see how much he had matured.
"We have to recognise that one of the main reasons why Jamie Roberts performed so well on that tour was because of the man outside him.
"Brian's really experienced and has an influence in the big games - we saw that again at the weekend.
"He scores a lot of tries and when it matter the big games step up to the plate."
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