Armed police entered Talbot's home in Greater Manchester, while he is currently abroad and believed to be sailing across the Atlantic Ocean.
The 63-year-old will meet with police when he returns to the UK, according to The Sun.
The investigation is related to a period when Talbot was a biology teacher at Altrincham Grammar School for Boys. Police are currently looking into claims of sexual abuse of pupils by staff in the early 1970s.
A Greater Manchester Police spokesperson said: "On 11 December 2012, police executed a number of warrants as part of an ongoing investigation into historic sexual abuse. The alleged offences relate to sexual abuse in the early 1970s, while the victims were pupils at Altrincham Grammar School for Boys.
"The offences currently under investigation did not occur within school grounds but allegedly involved a member of staff at that time. No arrests have been made at this time."
Talbot's agent Dave Warwick said that he has been unable to contact him, saying: "I'd like to thank The Sun for bringing this to my attention."
Talbot is currently a presenter for ITV Granada, and is most famous for his time as a weatherman for This Morning, in which he would jump across a large floating weather map at Liverpool's Albert Dock.