"It will be nice to see Alan," said Martinez. "He's a gentleman and a footballing person that everyone has huge respect for.
"He did a terrific job at our club in different roles and we wish him the very best of luck in his new project, but just not for this weekend."
Irvine spent three years at Everton as youth coach before succeeding Spaniard Pepe Mel as Albion manager in June.
"We had a lot of good work from him and his football vision and previously he had a very important job as assistant manager," Martinez told Sky Sports.
"We know a lot of the individuals there and obviously the manager (Irvine) had been a part of our fabric for a long time so you can imagine that there's going to be a lot of understanding between the two teams.
"But both realise it is a very important football game and we will need to be focused and put in a good performance for a positive result."
The managers will not be the only old friends on opposing teams.
Former England defender Joleon Lescott, 32, hopes to have recovered from knee and calf injuries to make his Albion debut - after moving from Manchester City - against the club where he made his name.
Everton hope to bounce back after losing 6-3 at home to leaders Chelsea in their last home match.
(Reporting by Tim Collings; Editing by Ken Ferris)
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