Assulin, 19, failed to secure a new contract at Barcelona - despite being regarded as one of Europe's most exciting talents - which put Spurs on red alert.
Harry Redknapp had been expected to secure the signature of the attacking midfielder, but the youngster could be tempted by a move to one of Spurs' London rivals, say Goal.com.
Assulin's agent Pini Zahavi said:
"The decision not to renew Gai's contract was mutual. At the moment we are considering his options."
The former Hapoel Haifa man become the youngest ever player to represent the Israeli national team when he made his debut in 2008 aged just 16.