Both Premier League sides are currently without coaches after Gerard Houllier resigned his post following serious health problems last week and Mark Hughes exercised a clause in his Fulham contract that allowed him to leave the club.
Villa were initially expected to invite Hughes to replace Houllier, but senior club officials insist that they have no intention of appointing the Welshman. Hughes, who has now gone through three Premier League managerial positions in four years had angered Fulham by courting the more affluent clubs while still under contract at Craven Cottage.
The 47-year-old was not Fulham's first choice to succeed Roy Hodgson last summer. Instead the club offered the position to Jol, under the mistaken understanding that the popular former Tottenham Hotspur manager was free to leave Ajax Amsterdam. Jol, who led Tottenham to consecutive fifth-placed finishes, has subsequently left Ajax and is interested in a return to London where he still owns a house.
Rijkaard returned Barcelona to Champions League success during a five season spell at the Camp Nou in which he also won two Spanish titles.
The former Netherland international contacted Villa last week to express his interest in replacing Houllier and is understood to have received a positive response.
Paul Faulkner, the Villa chief executive, has been charged with drawing up a shortlist of candidates for the position that is expected to also include Jol, Steve McClaren and Rafael Benitez. The club are also know to know admirers of David Moyes. The Scot has worked successive seasons at Everton without a transfer budget and could conceivably be tempted by Villa were the Midlands club to offer a long-term contract with significant funds to restructure their squad.
Hughes is represented by Kia Joorabchian, a controversial figure who has drawn the ire of several English and overseas clubs. On Friday, Joorabchian insisted that his client had not resigned from Fulham in the expectation of taking over at Villa. "He wants to go to club where he can fight for titles, whether that is in England, Spain, Italy or Portugal," Joorabchian said. "If that means he has to be out of management for a year then that is the case. Mark left Fulham because he wanted to explore his aspirations.
"I stick by what we are saying - we were not talking to anybody. No other club is in consideration. The timing may have influenced the press and public that he's headed in a direction. That's not the case."