The former Leeds United boss is Everton’s first choice to become their new manager after Frank Lampard was sacked.
Bielsa has held talks with Everton, but it was claimed that the Argentine rejected the job; he sees the team at Goodison Park as unsuited to his methods.
However, according to Argentine broadcaster TyC Sports, Everton are continuing to insist on Bielsa taking over.
The Toffees are convinced that Bielsa is the right man to instil discipline and levels of excellence at Goodison Park and want him in the dugout.
Another issue though is the financial demands that Bielsa would make.
It is claimed that Bielsa would be too expensive for Everton at present and it remains to be seen if there is any way for the Toffees to find a compromise.
Bielsa has been out of work since being sacked by Leeds last year, with the Whites appointing Jesse Marsch as his replacement.