Britain's Mirror newspaper said the changes would be to ensure drivers cannot sit out the decisive 'Q3' segment of qualifying, in order to save tyres and for other tactical and reliability reasons.
"Some believe a return to the free-for-all hour long sessions of the past is the answer because the current three-part formula has added nothing to the Saturday spectacle," said correspondent Byron Young.
The Telegraph's new F1 correspondent Daniel Johnson added: "To try and maintain the spectacle, (the) strategy group has asked the teams and the FIA to come up with ways of forcing drivers to go for the best grid positions in Q3.
"Plans likely to be discussed are believed to include supplying drivers with an extra set of qualifying tyres, specifically for the final part of the session," he added.
Not likely to get voted through in Bahrain, meanwhile, is an extension of Bernie Ecclestone's highly unpopular new 'double points' concept.
To keep the title alive until the end, drivers will score twice as many points at the season finale in Abu Dhabi this year, but F1's chief executive has written to the teams asking they vote for the concept to also include the preceeding two races.
Red Bull's Christian Horner, no fan of the concept initially, indicated he would support extending the scheme to three races because that would "take away an element of lottery over that last race".
But because the proposed change is occurring so late, it would require an unanimous vote, and there are reports the Mercedes-powered teams have no mind to support it.
Other teams are reportedly also not keen, a mischievous Lotus spokesman telling the BBC: "The best thing would be to make all the races double points."
The British media report added: "More than one top team believes it would be wrong to change the rules a month before the start of the season."