Villas-Boas has seen his future at White Hart Lane cast in doubt in recent days after the North London outfit slumped to a 6-0 defeat to Manchester City at the Etihad last weekend.
Enrique has since emerged as a candidate to replace the 36-year-old but the Barcelona legend has claimed that he will not break his contract with Celta - which expires in 2015 - despite the team struggling domestically.
"When I sign a contract I fulfil it," Enrique told reporters at a press conference. "We may be on the brink, but I see no reason why we should force any changes here. We'll continue to work along the same lines."
The 43-year-old worked alongside Spurs' director of football Franco Baldini with Roma during an ill-fated spell in the Italian capital.
Celta sit 15th in the Primera Liga standings, just three points clear of 18th-placed Real Betis.