I am on a permanent payroll with my agency and I want to change job asap. But my 2 months notice period clause is making my profile "unattractive" to recruitment agents whose clients always want the candidate "immediately on board". Should I resign first and look for a job offer so my availability becomes more and more "attractive" as I get closer to my employment end date;Or to be on the safe side wait for a job offer and then resign?
Also I want to keep good relation with my current agency for future references. So, would like to resign on good terms

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Most times recruiters ask if my notice period is negotiable.
What's the best way to negotiate the notice period with my agency for an early release?
Advise pls!!