Germany international Howedes played in every minute of their World Cup-winning campaign and Wenger is said to view the Schalke star as the man to provide competition to Per Mertesacker and Laurent Koscielny at the heart of the defence.
The 26-year-old's arrival would offset the departure of Thomas Vermaelen who joined Barcelona over the weekend for around £15 million.
A consistent criticism of Arsenal over the last few years has been their lack of a midfield presence with Wenger preferring to use more technically gifted players in the centre of the park, but the Frenchman is trying to address the weakness with a move for Wolfsburg spoiler Gustavo.
The Brazilian only moved from Bayern Munich to die Wolfe last year, but Wenger thinks that the 27-year-old would add some much-needed steel to an engine room that has been found wanting when coming up against muscular opponents.
Portugal international Carvalho is cut from a similar cloth to Gustavo, and has previously been linked with a big-money move to Manchester United and any potential deal for the defensive midfielder could cost around £30 million, with Sporting Lisbon unwilling to sell for a cut-price deal.
Arsenal have so far added Mathieu Debuchy, Calum Chambers, David Ospina and Alexis Sanchez to their ranks so far, with the combined fees costing over £60 million, and it is the signing of the Chile international that has excited fans.
Sanchez, a £32 million arrival from Barcelona, is seen as the missing piece to Arsenal's unsuccessful title challenge last term, when Olivier Giroud eventually succumbed to burnout after playing the majority of the campaign as a lone forward.
The Gunners begin their new campaign against Crystal Palace on Saturday evening fresh from beating title rivals Manchester City 3-0 in the Community Shield at Wembley on Sunday.