The former Rangers and England goalkeeper thought long and hard over the decision before finally allowing his head to overrule his heart, moving into a highly successful coaching career which has seen him serve Everton, Manchester United, West Ham United and currently the Scotland national team.
Woods was at Hampden on Saturday to see his old club win the Scottish Cup with a 2-0 extra-time victory over Hearts which included a sentimental late substitute appearance for veteran Rangers goalkeeper Allan McGregor.
The 40-year-old is out of contract next month and may be on the verge of retiring as a player. Woods can appreciate the emotions McGregor will be experiencing as he contemplates his future.
“He’s been a fantastic goalkeeper throughout his career,” said Woods. “He has won numerous awards and prizes over the years and he will look back on that and cherish it.
“I’m sure Allan could play on if he wants to. But I’m not sure if the Hearts game will be his final match or not.
“I remember when I stopped playing myself I was convinced that I could still play. But there comes a time when you realise it is over.
“It ultimately comes down to Allan and what he wants to do, whether that be give up or carry on for another year.
“If the Scottish Cup final is his final game then he can look back on a great career.
“He has stayed at the top for so long because he is that good.
“He looks after himself, he trains hard and when you do that then you earn more luck.
“When I say that I don't mean lucky saves, but you earn the luck to make the saves.
“Over the period of time playing for Rangers, it’s a bit more difficult than at other clubs.
“You aren’t involved in the game the whole time, so when you are called upon you have to make sure you do the right things.
“That’s a massive thing in terms of concentration and you have to learn how to handle that.
“Allan has done that over the years and continued to show it this season too.”
Jon McLaughlin, a Scotland squad goalkeeper, started the Scottish Cup final victory and Woods has backed the 34-year-old’s credentials to succeed McGregor as permanent first choice.
“It will be down to Giovanni van Bronckhorst whether Jon is the right man to be the Rangers number one,” he said.
“But he has produced great performances whenever he has been called upon.”
Woods, who won seven major honours during his five years as a Rangers player, was thrilled to see van Bronckhorst land his first piece of silverware as Ibrox boss at Hampden.
“Winning becomes a good habit to get into,” he said. “You have that one trophy and you want to get the next one and the next one.
“Looking to next season they will want to go one better in the league.
“Hopefully they can lift some more silverware as well.
“That’s why you come to a club like Rangers or Celtic, to win things and be challenging for titles.”