Mourinho failed to shake his opposite number's hand following a 1-0 win at the Liberty Stadium in April - a match that saw the since-departed Swansea defender Chico Flores dismissed for a second bookable offence.
But Monk says there are no hard feelings ahead of Saturday's top-of-the-table Premier League clash at Stamford Bridge.
"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 said. "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."
Before his snub by Mourinho, Monk had taken umbrage with the actions of Chelsea players and staff in the build-up to Chico's red card.
Explaining the situation, Monk added: "After Chico made the foul, there was a delay of around 20 or 30 seconds and it seemed the referee was not going to show the second yellow.
"Then their players surrounded the ref and their staff surrounded the fourth official and the second yellow card came.
"But Phil Dowd told me afterwards that he was just giving himself time to think and I accepted that. I have a lot of respect for him."
Swansea and Chelsea are the only two teams in the division to have won all three of their opening matches.
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