Michu took the Premier League by storm in his first season in English football in 2012-13 when he scored 22 goals following his £2million move from Rayo Vallecano.
The 29-year-old forward was capped by Spain and helped Swansea qualify for Europe by winning the Capital One Cup, but his second season was disrupted by injury and he scored only six times in 25 games.
Michu suffered another injury-ravaged campaign on loan at Napoli last season - making only five appearances for the Serie A club and failing to find the net once - and Monk has now announced the Oviedo-born striker will not rejoin his squad, despite having a year left on his Swansea contract.
"He won't be with the squad this year," Monk told the South Wales Evening Post.
"I spoke to him at this point last season, he wanted to go and felt that was right for him and I was happy to support him in that decision.
"I now think we have kind of moved on as a squad
We had a big transition last year."
Swansea finished a club-best eighth in the Premier League last season with a record points total and Monk has since strengthened his strikeforce by signing Ghana's Andre Ayew from Marseille and Portugal international Eder from Braga.
Monk admitted that he had left contact with Michu to Swansea chairman Huw Jenkins and the player could now return home to Spain, with reported interest from Granada and former club Rayo.
"I haven't spoken to Michu - there has been some difficulty with the numbers," Monk said.
"I have let Huw deal with his agent and that side of things.
"From what we hear from their side, I think Michu would like to try to move somewhere else.
"That's the impression I get, although I haven't had that conversation with him."
Source : PA
Source: PA