Arsenal and Spurs are thought to be the front-runners in the race for the England midfielder after his contract with Chelsea expired. Spurs boss Harry Redknapp has been quiet in the transfer market this summer although he has made no secret of his desire to sign Cole, who he brought through the youth ranks at West Ham.
"I think he is a great player and would be a great signing for us," said Bale. "If he did come obviously we would welcome him with open arms and he would be an important asset to the squad."
He added: "His Champions League experience would be an important asset for us. The more experience we have the better.
"A few of our guys have been in the Champions League before but for most of us it will be a new experience that we are looking forward to and if he can bring us more experience then that would be handy."
Redknapp has been mentioned as a possible successor to England manager Fabio Capello, whose future is under consideration following the Three Lions' humiliating exit from the World Cup.
Bale credits Redknapp with his emergence in the Spurs team and has urged the manager to stay at the club.
"I think the manager should definitely stay at Tottenham," said the Welshman.
"He did a fantastic job by taking us from low down in the table to the Champions League so I really don't want him to go. Hopefully he will stay.
"He gave me my chance and he was key to my development, especially towards the end of the season. We had a brilliant end of the season and hopefully the manager will stay so we can carry on this year."
Source: PA
Source: PA