Leeds' Italian owner had hoped to pair Monk with Barnsley number 2, Tommy Wright.
Cellino has been told that Monk wants his own man, a report claims
The report claims that Whites owner Massimo Cellino had hoped to pair Monk with the club's former winger Tommy Wright, who is currently employed by Barnsley.
However, Monk is said to have insisted on a reunion with Clotet before agreeing to replace Steve Evans at Elland Road.
Monk is said to want a reunion with Clotet at Elland Road
The 39-year-old, who worked at a number of clubs in Spain and Scandinavia before being hired as Swansea's academy consultant, is highly regarded within the game and was a reported manager target for Leeds' Championship rivals Brentford and Nottingham Forest earlier in the campaign.
In May 2014, six months after his arrival in South Wales, Clotet was promoted to the role of Monk's assistant, after the 37-year-old had taken permanent charge of the Jacks.
Monk was regarded as one of the country's most promising bosses at Swansea
And the Spaniard followed Monk out of the Liberty Stadium door last December.
Wright, who played for Leeds between 1982 and 1986, is a reported target for former boss Lee Johnson at Bristol City, having helped Barnsley to promotion alongside interim manager Paul Heckingbottom.
Wright, seen here (R) holding the League One play-off trophy aloft, was wanted by Cellino, a report claims