The 33-year-old goalkeeper has not featured in any United squad this term, after slipping down the pecking order before undergoing wrist surgery in November.
Ashdown's Elland Road contract expires in the summer and the former Portsmouth stopper seems poised to move on after posting on Twitter that he is likely to have taken part in his "last training session" with the club.
He tweeted: "Last training session today at #lufc. Great club. Look forward to my next adventure now. Thanks to all that helped me through injury."
Ashdown has not made a Championship appearance for Leeds since signing on a free transfer in 2012, but did play eight times in cup competitions in his role as understudy to Paddy Kenny.