Flores has flown out to Austria for transfer talks with the Qatari side and Monk is now planning for life without the Spanish star.
And the Swansea boss admits Flores's departure has come as something of a surprise.
Questions have been raised about Flores's future ever since Monk took the reins from Laudrup, for the pair clashed on the training ground when they were team-mates.
But from the moment he was installed as the Dane's successor, Monk made it clear that Flores would be part of his plans.
While the likes of Alejandro Pozuelo and Jose Canas have been marginalised by Monk, Flores was a regular under him last season and was favourite to start alongside Ashley Williams at Manchester United next week until a few days ago.
"I wasn't really expecting Chico to go," Monk conceded.
"I am a little bit disappointed, but I can't grumble with Chico at all. He has been magnificent with me since I took over — he did very well for me.
"He was a very good trainer and a very good player for us. But he came to us and said he wanted to go.
"No player ever leaves unless we say so, but I am only interested in people who want to play for Swansea City and I am not willing to work with anyone who doesn't want to do that."
Flores racked up 75 appearances in two seasons as a Swan and, though he had his troubles along the way, he will be fondly remembered because of his contribution overall.
He joined from Genoa in a £2 million deal, so Swansea will have doubled their money on Flores when his switch to Lekhwiya is finalised.
Now the challenge for Monk is to replace the 27-year-old, with the likes of Federico Fernandez and Virgil van Dijk both on Swansea's radar.
"When you look at what we paid for him, I think we have got a good deal for Chico and now we have to replace that quality with someone as good or even better," Monk added.
"That's the key for us now.
"And we have been looking at centre-backs all summer — we have been looking at all the positions throughout the squad because you have to be ready when something like this happens.
"Hopefully we can now replace Chico with a better player."
As things stand, Kyle Bartley and Jordi Amat are the contenders to play alongside Williams at Old Trafford in eight days' time.
Amat missed last weekend's friendly at Reading with injury, but has trained this week and should play some part when Villarreal come to the Liberty tomorrow (3pm). Leon Britton, Marvin Emnes and Jay Fulton all remain on the sidelines, with the latter currently closest to a comeback.