Even after beating Chelsea 2-1 in the final on Saturday, Wenger indicated he has to stew until tomorrow's board meeting before discovering whether his 21-year reign will be extended by the record 13-time FA Cup winners.
FA Cup semi-final - Mertesacker scored a crucial equaliser in the Gunners' 2013/14 semi-final victory over Wigan Athletic, but was forced off through injury against Reading a year later.
It was Wenger's seventh FA Cup victory since he joined the north London club in 1996.
Not being in the Champions League could potentially have an effect on player recruitment this summer - players might join a club that is in the tournament instead of Arsenal.
Confirmation of Wenger staying ends a turbulent period for the 67-year-old, who has been the lightning rod for criticism since the end of January as Arsenal's form plummeted amid speculation over his future. The contract offered by Stan Kroenke just needs to be approved by the club's board today.
Wenger led Arsenal to the FA Cup this season.
The pair went on to put in a superb showing as they contained Costa - who ended the season with 20 Premier League goals - until the 76th minute when the Brazilian-born Spain forward netted Chelsea's equaliser.
"It's very important to take two or three days to rest and also to be a bit relaxed after this season", Conte told the club's official website.
Arsenal will compete in the Europa League next season after failing to secure a Champions League qualifying position for the first time in almost two decades. "You can't do 35 years as a football manager if you think you are not the right man to do the job".
The Daily Telegraph says Conte has a drawn up a list of transfer targets that includes Everton striker Romelu Lukaku, Arsenal's Alexis Sanchez, Monaco's Tiemoue Bakayoko and Southampton centre-back Virgil van Dijk. "I don't know but for sure you must think that there is a lot of tension in those moments and sometimes you could be exhausted".
Some fans have become increasingly frustrated with Wenger's failure to win a Premier League title since the "invincibles" side of 2003-04.