Celtic claim a fee was agreed with Manchester City for John Guidetti prior to them taking the striker on loan.
Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
The former Barcelona coach was hired as an adviser nine months ago to help turn around the club's flagging fortunes but a first-round play-off exit this season does not appear to have impressed the club's owners.
The club released a statement which read: "The club has decided to terminate the services and consultancy with the company of Mr Johan Cruyff.
"This is because of not meeting the outcomes and objectives that have been established since the beginning of the contractual relationship.
"The coaching staff will not be affected, therefore technical director, trainer and technical assistants will continue to work with the club.
"The club thank Mr Johan Cruyff for the support and collaboration he has provided."