After failing to win any of his first six Premier League games in charge, the Spaniard was linked with a quickfire exit, but his team headed into the latest international break unbeaten in their last four top-flight outings.
Focus is now moving towards who he may bring in as part of a January squad update in January with Real Betis attacker Rodrigo Riquelme topping his rumoured wish list, as per TEAMtalk.
The 26-year-old has stood out for Manuel Pellegrini 's side so far this season, with three goals and two assists from 14 appearances, and that has caught Arbeloa's eye.
Serie A trio AS Roma, Napoli, Lazio and Como are also in the running, but Riquelme is under contract in Andalucia until 2030, and it would take an offer in excess of £20 million for Pellegrini to consider a sale.