Arsenal go into the final round of league fixtures in fifth, needing to beat Everton at home and hope either Liverpool or Manchester City slip up to allow them to gatecrash the Champions League places.
Adams played under Wenger for six years before his retirement in 2002.
"The board meeting is after the FA Cup final. Sometimes it [forces you] to make harsh decisions", Wenger said.
"In a football club today you have to employ people who can help you be successful".
"There are many aspects of a football club which has to be discussed at a board meeting".
"Of course I will be there".
Wenger, who had Adams working at Arsenal in the youth set-up for a short spell past year, said the remarks did not cause him pain and said he would rather focus his energies elsewhere.
Wenger has come under fire after a disappointing season that saw fans staging protests against him.
The Gunners are relying on an upset to secure Champions League qualification.
It goes without saying that the Frenchman has been under increased scrutiny this season, after yet another underwhelming campaign, which saw Arsenal once again fail to mount a serious Premier League title challenge.
As noted by ESPN FC correspondent Mattias Karen on Twitter, as seen below, Wenger dismissed questions about Adams by insisting that he didn't particularly give much importance to the former England international's thoughts.
"What is most important for me is to do the job well and finish the season as strongly as we can", he said.
With only one game of the season left, Wenger has continued to maintain secrecy over his future at the club and there are still no confirmations whether he will be signing a new contract.
Adams worked with the Arsenal Under-18s last summer, following Thierry Henry's departure, before moving on to be sporting director of Chongqing Lifan FC in the Chinese Super League.
The 50-year-old, who is now managing LaLiga side Granada, claims he tried to return to the club on four occasions in a coaching capacity, but was overlooked each time.
In it, he describes Wenger as 'essentially, not a coach'.