Newcastle Jets in training punch-up
Regan was involved in an altercation with goal-keeper Mark Birighitti during training at Ray Watt Oval on Monday.
While it's not known exactly what spared the flare-up, it left Regan with a nasty split above his left eye.
A number of team-mates were forced to step in to separate the pair as the session was temporarily halted, before Birighitti headed for the sheds shortly afterwards.
The pair were hauled before club officials following in the hours after the angry spat, with Jets CEO confident the issue was resolved and revealing the players had been dealt with.
"You want your players to have a competitive nature and show passion on the field because that's a key ingredient for success in any sport," Middleby said.
"However, it's important they don't cross the line and let their emotions get the better of them.
"As a club, we've spoken to both Mark and Taylor about the incident and have dealt with the matter internally."
While the Jets have ensured a rather difficult A-League campaign, it's a surprise this sort of incident comes on the back of a two-game winning streak that has breathed life into their finals hopes.
They sit just one-point behind the Central Coast who are in sixth spot ahead of this weekend's F3 derby at Bluetongue Stadium.