Januzaj arrived in San Sebastian in 2017 and has played 167 games for the club, scoring 23 goals.
He was part of the team that lifted the Copa del Rey and has played three Europa League campaigns for the Basque outfit.
Monreal joined La Real in 2019 and has played 69 games for the club, scoring four goals. He was also part of the Copa-winning team and played two Europa League campaigns for the club.
La Real finished the 2021/22 La Liga season last night with a 2-1 defeat to Atletico Madrid.
They finished sixth in the table – three points clear of seventh-placed Villarreal and three behind fifth-placed Real Betis.
Making up the eight-point gap between themselves and Sevilla in fourth will be the challenge for next season.