Negotiations over a settlement for the rest of his contract have since stalled with Sinnott believed to want the fee paid in one lump sum but Vale understood to be keen on staggered smaller payments.
Sinnott claims Vale failed to meet a legal deadline last Friday - after which he took the manager's job at Unibond Premier Division side Bradford Park Avenue - and he has been left with no option but to take the matter to court.
He told his new club's official website: "My decision to take up the reins at Bradford Park Avenue was made after 4pm on Friday January 16 when Port Vale again failed to meet a legal deadline. After consultation with my legal representatives, Russell Jones & Walker, we feel we have no option but to proceed with court action against Port Vale."
Vale chairman Bill Bratt added in The Sentinel: "We have honoured the contract and Lee has been paid as and when a payment has been due, and we would do that until his contract runs out. I have tried to contact Lee over the past couple of months but I have been unable to do so. I would like to meet him face-to-face to sort it out."