The Wales international’s situation has been a constant source of speculation in recent days after he admitted that he would be considering his future this summer.
However, those comments after the Champions League final came before Zinedine Zidane stood down as Real Madrid boss to leave the Spanish side looking for a new manager.
Manchester United have been strongly linked with a move to sign Bale since his comments about his future.
However, Burley feels that the 28-year-old would be wise to see how things play out at Real Madrid before making a decision about his future.
Burley told ESPN FC: “I am adamant he should see what they do in terms of appointing a new manager and take it from there…”
Meanwhile, Manchester United have already begun their summer recruitment drive by securing the signings of both Diogo Dalot and Fred last week.
The Red Devils are believed to be on the lookout for a number of new signings this summer as they look to try and assemble a squad capable of winning the Premier League title next season.
Manchester United finished second in the Premier League and without a trophy last term.
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