Allen believes Real Madrid will already be watching the midfielder after the way he has started this season.
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He told Tottenham News: "He has his best years ahead of him. Tottenham needed to tie him down to a long-term contract because clubs like Real Madrid will be looking at him: they will show interest.
"So they will do well to keep him, I think."
Bergvall famously turned down an offer from Barcelona, while in the city, to commit to Tottenham two years ago.