A Premier League arbitration panel has been asked to rule on a clause in the 22-year-old full-back's contract which the Magpies believe triggers his release for a fee of ?1million.
Toon bid denied: Swansea are keen to keep hold of Taylor
The promoted Swans insist the clause only allows clubs to talk to the player and that they do not have to accept any offer.
As a result, they rejected Newcastle's bid out of hand last month and with the Tyneside club unwilling to pay any more than that and Taylor's current employers placing a significantly higher valuation on him - some reports have suggested as much as ?10million - the situation has reached stalemate.
In demand: Liverpool and Arsenal are interested in Enrique
It is understood the Premier League have been asked to intervene, although that request has not come from there Magpies, who are maintaining a watching brief.
No date has yet been set for a hearing which could have wider implications for clubs and players who have agreed similar clauses.
Newcastle boss Alan Pardew as targeted left-back Taylor, who joined Swansea from Wrexham for an initial ?150,000 in June last year, for some time.
However, Pardew does not see Taylor as a direct replacement for Spaniard Jose Enrique if widespread interest in him results in a move.
Pardew is desperate to keep the former Villarreal man at St James' Park amid speculation that clubs including Liverpool and Arsenal will try to lure him away, and to provide him with competition for his place.
However, Newcastle are not prepared to become involved in a bidding war for Taylor and will look elsewhere if the player and Swansea cannot resolve their differences.
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