The Spaniard, who spent four years with Hearts before signing for Alaves in 2011, is a free agent following a spell in Finland with Honka.
Despite Thistle's attempts to lure the player back to Scotland, Palazuelos looks likely to join Championship side Yeovil.
Archibald said: "We had a chat with him but he couldn't do anything about it. He decided to go elsewhere."
Meanwhile, Archibald will not be attempting a first-team return against Motherwell on Saturday after playing for the U20s in a 2-2 draw with St Johnstone.
The 36-year-old defender said: "It was good to get back out there. I think it was the first time in a year.
"We had a wee bit of a crisis with our centre-halves in the 20s. I just thought I would help them out.
"I don't know if I really helped them out to be honest, I think I was to blame for two goals."