The idea to bring back refuelling, which was last used in 2009, came out of a rule-making strategy group meeting of leading teams and officials.
But further talks this week have revealed major opposition, with teams concerned about the costs.
There will be an analysis of its effects on the show before a final decision.
F1 is pressing ahead with other changes planned for 2017 to speed up the cars.
"It is going to be back to the quickest cars on the planet with the most efficient energy usage, with wider tyres, with driver aids removed, with driver-controlled starts back again," said Mercedes F1 boss Toto Wolff. "There is so much good stuff happening."
Refuelling was proposed during the strategy group meeting as a way of making the cars lighter and therefore faster for more of the race duration.
But none of the teams are in favour of refuelling, which was banned on grounds of cost, safety and because it reduced the amount of on-track overtaking.
A meeting of sporting directors in Monaco on Friday concluded that refuelling would add about a million euros to each team's annual budget. Several smaller teams are struggling to make ends meet at the moment.
The teams are to do further analysis on the effects re-introducing refuelling would have on the racing. The findings will be presented at a meeting at the next race in Canada on 5-7 June.
Statistics show that the years during the refuelling era of 1994-2009 produced consistently the lowest number of overtaking manoeuvres on track per race of any year since 1980.
Regardless of whether refuelling returns, F1 cars will be made five to six seconds a lap faster than current speeds.
Full qualifying results
Monaco practice results
Proposals to reintroduce refuelling into Formula 1 are likely to be dropped because of a lack of support.