Former General Electric CEO Jeff Immelt used to fly with two corporate jets when he would travel, a nearly empty jet following the one Immelt was traveling in, according to a report in The Wall Street Journal.

The Journal, citing sources familiar with the matter, reported that the extra jet was utilized in case there were any mechanical problems with the one Immelt was in.

At times, the alternative jet would park at a distance from the other one to avoid attention, the paper added, and crew members were discouraged from discussing Immelt's travel arrangements.

A GE spokeswoman told WSJ the "two planes were used on limited occasions for business-critical or security purposes." GE did not immediately return CNBC's request for comment on jet use.

The revelations came amid a broader WSJ report about new CEO John Flannery's cost-cutting and efficiency measures to reshape the conglomerate.

GE had spent $258,000 on Immelt's jet travel last year, with an additional $75,000 for other top executives, the newspaper said. Flannery took aim at the GE air fleet as one of his first cost-cutting initiatives.

Read the full WSJ story here.