A photograph, which has been widely shared on social media, showed the message "love from Manchester" on a Paveway IV bomb loaded on a British jet carrying out air strikes from Royal Air Force (RAF) Akrotiri in Cyprus, The Telegraph reported.
An RAF spokesperson confirmed that the photo was genuine. "The sentiment of the message written on the weapon is understandable and such writing has history in the RAF, so the individual concerned will not be taken to task," a source was quoted as saying.
The report comes days after suicide bomber Salman Abedi blew himself up at a concert by pop star Ariana Grande at Manchester Arena last week, killing 22 people and 119 injured.
Children as young as eight and parents were among the dead after thousands of fans were targeted as they left the gig on Monday.
During World War II, army men wrote messages on bombs headed toward Japan after the Pearl Harbor attack. Messages were also written on bombs after the 9/11, with notes coming from New York City police and fire departments.