The 35-year-old's future has been the subject of much speculation, but it is understood that he will now put pen to paper on the extension when he returns from from a five-day training exercise with the England squad in Portugal.
Negotiations were said to have hit a snag over Lampard's basic £150,000-a-week salary, but it is believed that the England midfielder will now take a pay-cut with appearance-based incentives.
The publication quotes a source as saying: "Frank is feeling very positive about the whole thing. He fully expects his Chelsea future to be resolved at some point next week before he flies off to Brazil."
"He is not looking at any other option other than spending next season at Stamford Bridge."
Lampard, who is the highest-scoring midfielder in Premier League history with 171 goals, will join teammate and Chelsea captain John Terry in extended his stay at Stamford Bridge.
Former England captain Terry agreed his own fresh terms last week, but it looks as though Ashley Cole will be heading for the exit door this summer.
Lampard's influence is not as great as it once was, but manager Jose Mourinho still sees the midfielder as an important member of his squad, and is believed to have been keen to see the veteran ink a new contract.
England boss Roy Hodgson also sees Lampard as vital to his Three Lions set-up, and included him in his 23-man squad for the World Cup.
Hodgson, alongside Steven Gerrard and Wayne Rooney are three who can provide some big-tournament experience to a youthful-looking contingent that will travel to Brazil next month.
Chelsea finished third last year behind eventual Premier League champions Manchester City and runners-up Liverpool.