"I spoke to (Mercedes motorsport head) Toto (Wolff) and (technical head) Paddy (Lowe) about an invitation for Sebastian and they are easy with it," he told his followers on Twitter on Tuesday.
"Dear Seb, this is the official invitation to join our debrief Friday 16.00 at Sepang. See you there, don't forget your notebook!," he added.
The two Germans had exchanged banter in the post-race news conference at the season-opening Australian Grand Prix after Rosberg suggested he would like to see Vettel and other rivals close the performance gap to Mercedes.
"I think in the next couple of races we’re going to be leading the way for sure, and we’re going to try and keep it that way, but we know it would be good if they can come a bit closer, as long as they don’t come too close," Rosberg said.
Vettel, who is not on Twitter and finished third in the race, took that with some scepticism.
"Be honest. Do you really hope so? Seriously? You finished 30 seconds ahead of us and you hope it’s going to be closer? So you hope you slow down? Is that what you’re saying?," asked the four times world champion.
Rosberg replied that he hoped his compatriot could give himself and double champion team mate Lewis Hamilton, winner in Melbourne, a challenge for the good of the sport.
"Half of me –- or a part of me –- thinks about the show because I want to give people a great time at home watching on TV or at the track. If you do come a bit closer, that would be awesome for everybody," he said.
Vettel jokingly suggested that Mercedes might like to open their garage to everyone in Malaysia, to which Rosberg replied that he would invite him.
"OK, thank you for the invite, I’ll come," said Vettel, who joined Ferrari from Red Bull at the end of last year.
"Friday Malaysia, OK," retorted Rosberg.
"Engineers room? Debrief, I’ll be there," promised Vettel.
Champions Mercedes, who won 16 of 19 races last year, finished one-two in Malaysia after securing their 12th pole position in a row.
The Malaysian Grand Prix is on March 29.
(Reporting by Alan Baldwin, editing by Justin Palmer)
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