He will replace Tom Loxley, who resigned last month, having edited the title for more than four years.
Dennis Publishing would not confirm the appointment, but it is reported that Gutfield flew to London two weeks ago to meet Dennis Publishing's London management.
Gutfield edited Stuff for three years, during which time he saw the title's subscription base grow to 1.2 million.
In May last year, he stepped down from the position, to be replaced by the editor of the US edition of Maxim, Mike Hammer. Gutfield took on the non-editorial role of brand communications director. Previously, Gutfield wrote a column called The Greg Show for Jack. Dennis Publishing bought the title last year for £5.1 million.
Over the past four years, under Loxley, Maxim delivered its top circulation of 328,000. Recently, it has not fared as well and Loxley said somebody prepared to commit themselves "for the long haul" should take over.
Maxim's current ABC circulation figure is 243,341, down 3 per cent from last year. The fear is that this decline is set to continue with the introduction of IPC's and Emap men's weekly titles, Nuts and Zoo Weekly.