However, the cheeky suggestion did not go down well with some passengers, who took to Twitter to complain about the napkins – with one describing them as "creepy AF".
"Pretty sure no one appreciated unsolicited phone numbers in the 'good old days' and they sure as heck don't want the number of someone who has been gawking at them on a plane for hours today. Not a good look," @ducksauz wrote.
"Napkins received from @Delta on Wednesday flight seem unintentionally creepy, especially after reading the smaller print. Swing and a miss, @DietCoke," another passenger, @MJJoe, wrote.
"Anyone else see these awful @Delta in-flight @DietCoke napkins? There's a spot on the back to put your name and phone number to give to your 'plane crush,'" @LMCatalano wrote.
Delta Air Lines has since apologised for the napkins.
"We rotate Coke products regularly as part of our brand partnership but missed the mark with this one," a Delta rep told INSIDER. "We are sorry for that and began removing the napkins from our aircraft in January."
Coca-Cola also offered an apology.
"We sincerely apologise to anyone we may have offended," the spokesman said.
"We worked with our partners at Delta to begin removing the napkins last month and are replacing them with other designs."