Mourinho refused to shake Monk's hand following a 1-0 Chelsea win in a fiery encounter at the Liberty Stadium in April.
Both managers are poised to face off again in this weekend's top-of-the-table clash, but Monk insists that he has nothing but respect for the two-time Champions League-winning coach.
"He didn't shake hands with me after the last game, but I am probably not the only one and it's not a big deal," he told reporters. "I like to shake hands and finish things well at the end of a game, and of course I will shake his hand this weekend.
"He is a top manager, someone who is hugely respected in football. He has won titles at the highest level and is in the top bracket - he has legendary status as a manager.
"He is winning things on a regular basis and he has managed some of the top clubs in Europe. He is someone for someone like me to look up to."
Swansea sit behind the Blues on goal difference after both picked up maximum points from their opening three Premier League outings.
Saturday's clash is scheduled to kick off at 3pm.