The incident, which is also being investigated by police, took place after last month's Old Firm match, live on Sky Sports, as McPherson approached Alonso on the pitch at Broadwood Stadium.
The 52-year-old has already apologised to Alonso for the incident, describing his behaviour as "out of character".
In a statement earlier this month he said: "I know I have severely let myself, our team and the club down. I hold myself to the highest of standards and have never done anything like this before in a long coaching career, and I know I fell way short of that with my actions.
"This club is also built on incredibly high standards, and I have already apologised to the board, the football staff, and our fantastic group of players who I care about dearly.
"I would also like to apologise to the Rangers fans as I am aware of what a privilege it is to represent this club in any capacity, and I am sorry that on this occasion I did not uphold the standards this club demands.
"I also understand how exciting a time it is for the women's game in Scotland, which I have come to care passionately about, and I apologise for any negativity my actions have brought in our attempts to grow the game."
