The former Roma coach was linked to the position, currently held by under-fire manager Andre Villas-Boas, by British media in the wake of Tottenham's 6-0 loss to Manchester City.
But Enrique said he had no intention of leaving La Liga, wanting to see out the two-year contract he signed in June.
"When I sign a contract I fulfil it," the Spaniard told a news 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."
Enrique's Celta Vigo side sit 16th in La Liga ahead of a crucial home clash against Almeria, who are in the relegation zone, on Saturday.
"Almeria are a direct rivals of ours, so this match is worth more than three points. It's very important for us," he said.
"We have to be patient. Almeria will present many complications, but we can't be ponderous. We can't go into the match with any doubts."
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