Monk escaped a Football Association charge on Wednesday for his post-match outburst at Stoke on October 19 when he described Potters winger Victor Moses as "a cheat" for falling inside the penalty box and called referee Michael Oliver's decision "disgusting" for awarding the spot-kick.
The Swans boss has been unhappy with what he sees as big decisions consistently going against his side this season, the latest coming on Tuesday night when Argentina centre-back Fernandez was sent off in stoppage time of the 2-1 Capital One Cup defeat at Anfield.
Monk's concerns have led to the setting up of a meeting between him and Riley, the general manager of the Professional Game Match Officials Limited, and he is keen to put his views across while getting feedback from referees.
"I spoke to Mike on the phone last week and I'm going to meet him face-to-face on Friday," Monk said.
"I'm just going to give him some concerns I've had and get feedback from him.
"It's a general discussion on how the season's been from our side of things as well as getting the referees' views as well.
"There's no agenda, it's just getting points across."
The FA decided to take no action against Monk for his post-match comments at Stoke but the governing body told the Barclays Premier League's youngest manager to be careful in his dealings with the media straight after matches in future.
"I felt in my mind I spoke the truth after the game," Monk said.
"I didn't expect to be punished because I felt I didn't say anything out of turn which warranted that outcome.
"It's nice to see the FA has come to that outcome but they said to me to bear in mind after the game, albeit at an emotional time, to be wary of whatever you say.
"I generally am, I am conscious of what I say and thought I did that at Stoke and, with no charge, the FA saw it that way as well.
"I wasn't out of control, but sometimes when you feel strongly about something you say those things
But I stand by what I said."
Monk was further frustrated in midweek when Fernandez was shown a straight red card by referee Keith Stroud for a tackle on Philippe Coutinho with the fourth round tie balanced at 1-1.
The challenge was deemed as serious foul play and Fernandez faced a three-match ban, starting with Saturday's league trip to Everton, but the 25-year-old is now free to play at Goodison Park.
"Swansea City can confirm that the Football Association has rescinded the red card shown to defender Federico Fernandez against Liverpool in midweek," a club statement said on Thursday evening.
The Welsh club appealed against the decision with a written statement and video evidence before an FA appeals panel overturned the red card.
Source : PA
Source: PA