I'm completely focussed on getting things ready for the new season with Huddersfield Town.
The former Bradford City and Huddersfield Town player has experience of the Unibond League with Farsley.
Wadsworth was sacked from his post at English third division side Huddersfield Town in March.
"Every time I have played Huddersfield Town I have been impressed with their team, " Kay told the Terriers website.
Hundreds of football fans plan to protest against "draconian" ticket and travel restrictions for Hull City's game at Huddersfield Town.
BBC: Football fans to stage protest over police restrictions
The 42-year-old told BBC Radio Leeds he is keen to get back into management and Huddersfield Town would interest him.
He is believed to have got into the bin near the bus station in Huddersfield town centre at about 04:45 GMT.
Dover Athletic, under previous manager Martin Hayes, beat Gillingham and Aldershot before losing to 2-0 Huddersfield Town in the third round.
Amanda Jacks, from the FSF, said up to 300 people, including Huddersfield Town supporters, are due to take part in the demonstration.
BBC: Football fans to stage protest over police restrictions
And captain Anthony Kay left the club for Huddersfield Town last week.
Loan periods at Bradford City, Barnsley and Huddersfield Town followed before he moved to Sheffield Wednesday in 2008 where he made only seven appearances.
Gus Poyet's men have 83 points with eight games left, 13 clear of second-placed Huddersfield Town and 16 clear of the teams outside the play-off pack.
BBC: Brighton targeting 100 points, says midfielder Bridcutt
Restrictions were imposed after the kick-off time for the match at Huddersfield Town's John Smith's stadium was changed to 17:20 GMT to allow Sky to broadcast the game live.
BBC: Football fans to stage protest over police restrictions
Rothery, 19, made his Carlisle debut in the Easter Bank Holiday Monday defeat at Huddersfield Town, having joined the club on a trial basis during the January transfer window.
Last month, he joined League One club Huddersfield Town on trial and was given a run-out in their reserve match against Rotherham United, scoring the opening goal in a 2-2 draw.
"Indeed, I think the records will show that during three spells as manager he has probably one of the finest records ever achieved by a manager of Huddersfield Town, " he added.
When he retired from playing in 1949 he moved immediately in to management at Carlisle United, later moving to Grimsby Town, Workington and then Huddersfield where he was spotted by Liverpool chairman T.
Protestors are expected to meet at Huddersfield Railway Station at 13:45 GMT before marching to the town's Piazza shopping centre.
BBC: Football fans to stage protest over police restrictions
Meanwhile, Northampton Town have said they have not had an approach from Huddersfield to talk to their manager Stuart Gray.
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