Pressure has intensified on the national team boss after a 2-0 defeat to Belgium left the Scots bottom of their World Cup qualifying group. Scotland have taken just two points from four games - the only nation in the section without a win so far - and have little hope of booking a place at Brazil in 2014.
Levein has made it clear he has no intention of quitting and the SFA will assess the situation over the coming days. Regan told BBC Scotland: "Now is not the time to be making announcements and decisions. That's something that'll happen over the course of the next few days."
He added: "It's important to look at the situation and allow those involved to actually put their thoughts across the table. It's important that we actually sit down, look at the facts and then decide on the next steps. When we've had a chance to do that then we'll decide what happens next."
Levein still has the backing of a number of his players and defender Christophe Berra believes the SFA need only consult the squad to determine the feeling within the camp.
He said: "They just need to ask the players. The players enjoy turning up, there aren't as many call-offs as there used to be in the past. We've got a bright group of players and we are all fighting for the right cause. There is no-one turning up who isn't giving 100%. We all are.
"In club football, international football, whatever line of work you are in, if you're not getting results, there is going to be speculation that puts people under pressure. The boys like working under the manager and I think he's done well for us.
"I know it's a results-based game but we think, at the moment, we've got one of the most talented Scottish groups for a long time. In the end, we are the ones who go on the pitch and try to win the games."
Berra's thoughts were echoed by James McArthur, who wants to see Levein remain at the helm and for the players to shoulder more responsibility.
The midfielder said: "I would love him to stay. I think he's a brilliant manager. He has done everything right by the players. The players think he's very good and we are just unfortunate that we've not got the results. It's down to us players, we should be getting the results. The gaffer is putting us out there and we're not doing it - that's all I can really say about that."