Holding had been thought to be surplus to requirements at the Emirates and available for transfer this summer, with the likes of Newcastle also interested in his services.
However, the centre-back started the Community Shield as Arsenal beat Liverpool and played 90 minutes of the opening game of the season as the Gunners kept a clean sheet in a 3-0 win over Fulham.
There is plenty of competition in the middle of defence at Arsenal, especially since the signings of Gabriel Magalhaes and William Saliba, but Holding appears to be confident in the fight for his place.
The Sun reports that the 24-year-old is ready to turn down a short-term move to West Ham, even if Arsenal were prepared to accept the substantial loan fee on offer.
Holding’s chance to prove himself to manager Mikel Arteta is set to continue with Shokdran Mustai, Pablo Mari, Sokratis Papastathopoulous, David Luiz and Calum Chambers all out injured.
Holding appears to have climbed up the pecking order, though, and is likely to start on Saturday against West Ham, who will have to contend with what they have missed out on.
David Moyes’ side got off to a really poor start to the season last weekend, losing 2-0 at home to Newcastle and the Scot is desperate to add to his central defensive options, having tried and failed to sign Burnley’s James Tarkowski earlier in the summer.