Sources in LG's office said a "final decision" on the political situation is likely to be taken at the earliest based on views of the three political parties.
Jung first invited BJP for talks on whether it is interested in taking a shot at the power, being the single largest party in the Assembly.
Sources in BJP said the dominant view in the party is that it should go for polls and not take power by "manipulation" as Prime Minister Narendra Modi's rating was still going "high" and enthusiasm among the party workers has increased following victories in assembly elections in Maharashtra and Haryana.
"We are preferring elections. There is little possibility of the party forming a government in Delhi," a senior Delhi BJP leader told PTI, adding a final decision on the issue will be taken by the top leadership in a day or two.
Earlier, Delhi BJP Chief Satish Upadhyay and Union Minister Harsh Vardhan called on Jung. The meeting was described by the party as "informal".
The Lt Governor also invited AAP and Congress for talks on government formation although both the parties have been demanding fresh election and accused him of acting at the behest of BJP.
Both Congress and AAP have been maintaining that they were fully ready for fresh elections and accused BJP of running away from polls for "fear of defeat".