Sky Sports presenter Jones joined the club’s board in a non-executive role in December 2019.
Sunderland have requested more tickets for Saturday’s game after their allocation of 43,960 within minutes of going on general sale on Monday morning.
This was an increase of around 6,000 on the club’s initial allocation, which had sold out by Friday.
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Sunderland warned last Friday that they had been told any further increases were unlikely.
Wycombe had supported that initial increase in a bid to prevent Sunderland supporters purchasing tickets for their end. The Chairboys said last week that they were close to selling out their initial allocation of 19,205, and were expecting to be given more.
Even so, that would still leave a significant portion of the ground unsold as it stands.
Jones wrote on Twitter: “So EFL as things stand there will be 20,000 empty seats @wembleystadium when @SunderlandAFC play @wwfcofficial.
“That is not a good look for anyone! Please let us have another 10,000 at least.”
A statement from Sunderland AFC on Monday morning said: “Sunderland AFC tickets for the Sky Bet League One Play-Off Final are now sold out.
“Less than a week after the Black Cats' semi-final victory over Sheffield Wednesday, over 43,960 tickets have been sold for Saturday's Wembley Stadium showdown against Wycombe Wanderers.
“SAFC has made a request to the EFL and Wembley Stadium to further increase the club’s ticket allocation and an additional update will be issued in due course.”