Both managers have clashed in the past and will meet again on Sunday, in what is the competition's only all-Championship clash of the fifth round
Clough and Nottingham Forest boss Davies clashed in a feisty east Midlands derby at Pride Park back in 2010 during the Sheffield United manager's tenure in charge of Derby County.
Scotsman Davies reported the former Forest striker to the League Managers Association after claiming Clough kneed him in the back in a touchline altercation during Derby's 1-0 win. The 49-year-old is also a former Derby manager himself.
Clough was sacked by Derby following a 1-0 defeat at the City Ground in September and has since been charged with the task of turning around League One strugglers United's fortunes.
The 47-year-old's main remit is to ensure the Yorkshire club avoid relegation as they sit in the relegation zone but shock FA Cup wins at Premier League sides Aston Villa and Fulham have gone a long way to raising morale at Bramall Lane.
And a fifth-round victory over his former club Forest and old adversary Davies on Bramall Lane on Sunday would be equally sweet for Clough.
He said: "I don’t especially get on with him [Davies], no. We will shake hands and that will be it.
"We have had a few run-ins down the years, which is probably inevitable because of the teams we were managing at the time.
"Derby versus Forest clashes are always going to be interesting. When I was at Derby, they included days when we had melees and we all got fined by the FA. There was a lot of passion on show. Up until the most recent game in September, we had a good record at Derby."
A last-gasp extra-time goal from Shaun Miller at Craven Cottage ensured United made Fulham their second top-flight scalp of the season as the third-tier side claimed a stunning 1-0 win during a fourth-round replay.
Championship promotion-hopefuls Forest, meanwhile, needed a replay to see off Preston North End in the fourth round but Clough knows his side will have to upset the odds in order to reach the last-eight.
He said: "We are the lowest-ranked team left in the competition and we are up against a team going for promotion to the Premier League."
Forest make the short journey north on the back of a 16-game unbeaten run and will be eyeing a place in the quarter-finals for the first time since 1996.
Midfielder Guy Moussi picked up a calf injury in a 3-0 midweek win at Huddersfield Town and may miss out, while Eric Lichaj (groin) is definitely out.
Henri Lansbury (back), David Vaughan (knee), Kelvin Wilson (back), Dexter Blackstock and Chris Cohen (both knee) are long-term absentees.
United captain Michael Doyle is back in contention after serving a three-match ban for the red card he was shown in the first game against Fulham. But on-loan striker Billy Paynter is cup-tied after playing in the competition for parent club Doncaster Rovers.