The Spaniard has until Monday to respond to the FA.
His rivalries with Guardiola - whose side, now eight points clear of United at the top of the Premier League, United play at Old Trafford on December 10 - and Gunners boss Arsene Wenger are both well documented.
I can not control myself.More news: Former Yemen rebel ally Saleh calls for talks with Saudi Arabia
Guardiola courted controversy on Wednesday evening after gesticulating on the pitch with Redmond following City's late win.
"When you spend 400 million or more in last two years, expect teams to defend as they can't compete on normal terms with you", Roberts concluded.
Speaking at a news conference to preview Sunday's Premier League game against West Ham, Guardiola was asked whether he regretted his actions and simply replied: "Yes". "I didn't know him last season, I realised how good he is" was what Guardiola claimed before Redmond came to his support.
'I told him I was doing what my manager had asked.More news: Tiger Woods Cards Opening Round 69 at Hero World Challenge
"That is not your job it's his manager and what you want them to do just let them open up so you can score a lot? Yes he was very passionate, intense and aggressive but he was only very complimentary and positive to me".
However, the matchup turned out to be far from a straightforward one for Guardiola's men, with Oriol Romeu's equaliser 15 minutes from time having thrown a spanner in the works for the Premier League table-toppers, following Kevin De Bruyne's opener in the 47th-minute. Hojbjerg told Redmond such behaviour was not unusual and, if Guardiola liked a player, it did not matter whether they played for his side. "It's the same as I do to beat them".
Redmond explained that "nothing negative or offensive was said towards me" and concluded: "Sadly this story is an example of lazy journalism and is a complete joke".More news: Tennessee parts ways with AD John Currie amid tumultuous coaching search