The north London side have been linked with a host of players this summer as Arsene Wenger looks to prepare his team for the 2017-18 campaign.
However, despite all of the speculation, the Gunners have only completed deals to bring in Sead Kolasinac and Alexandre Lacazette so far this summer.
The Gunners have been linked with a move to bring Monaco midfielder Thomas Lemar to the club, while Alexis Sanchez’s future continues to be a source of speculation.
But Groves believes that Arsenal’s defence needs strengthening if they are to improve on their fifth-placed finish last term.
And the former Arsenal star feels that a new defender and midfielder should be the Gunners’ next two signings.
Speaking in an interview with bwin, Groves said: “Arsenal proved with their fourth, fifth or sixth choices in the FA Cup final that they can deal with absences at the back.
“Per Mertesacker, Rob Holding and Monreal or Kolasinac can deal with the situation short-term, but then Mustafi and Koscielny will be back in the fold.
“I do think Arsenal need another centre-half and another top-quality midfielder to help defensively.”
Arsenal are currently gearing up for their Community Shield clash against Chelsea at Wembley on Sunday afternoon.
The north London side beat the Blues to win the FA Cup at Wembley back in May.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news