Newcastle recently signed striker Gayle from Crystal Palace and winger Ritchie from Bournemouth.
Gayle played in the Championship with Peterborough United, while Ritchie featured in the second tier of English football with Bournemouth.
It has been reported by The Northern Echo that Newcastle manager Benitez successfully targeted the duo due to their experience of Championship football.
Newcastle got relegated from the Premier League at the end of the 2015-16 campaign and will feature in the Championship next season.
The Magpies will be one of the favourites to finish in the top two, but they will not find it easy.
Newcastle have also signed 24-year-old goalkeeper Matz Sels from Belgian club Gent in the summer transfer window.
Gayle scored three goals and created eight chances in 16 Premier League appearances for Palace last season.
During the 2015-16 campaign, Ritchie scored four goals and created 40 chances in 37 Premier League games for Bournemouth.