The former Real Madrid coach replaced Marco Silva during the summer but has struggled to deliver the results expected after Fulham came close to securing European qualification last season.
After six league matches, Fulham remain without a victory and sit at the foot of the table. Their disappointing start has increased scrutiny on Arbeloa, although the Spaniard maintains that worrying about his own position would be counterproductive.
“I never worry about my position,” he told the BBC.
“I don't feel fear. You cannot be a coach if you feel it. You have to work, make decisions and show confidence in your players.”
Arbeloa's comments came amid growing concern about Fulham's results and their inability to see out matches. The London club have collected only two points from their opening six fixtures, leaving them in need of a significant improvement.
Their latest disappointment came against Ipswich Town, where Fulham appeared poised to secure their first league victory of the campaign before conceding twice late on to lose 2-1. Ryan Sessegnon had put them ahead, but goals after the 88th minute turned the match around.
It was the second consecutive league game in which Fulham had surrendered a late advantage, intensifying questions about their ability to manage the closing stages.
Arbeloa, however, insisted that the club's fortunes mattered far more than speculation about his employment.
“The club's position is the most important thing,” he said.
“It is not about my position, but about Fulham's position. That is the most important thing. Of course, it is only six matches, but it is true that we need points.”
The manager's comments reflect the immediate priority facing Fulham: turning performances into victories before the pressure surrounding their league position becomes more severe.
There has also been speculation linking Brentford manager Thomas Frank with a possible move to replace Arbeloa. However, the Fulham boss has a contract running until the summer of 2029 and has publicly maintained his focus on improving the team's results.
The challenge is considerable. Fulham must address their late defensive lapses and find greater consistency if they are to climb away from the relegation zone.
Their upcoming fixtures against Hull City and Coventry City offer opportunities to collect valuable points against newly promoted opposition. Failure to take advantage of those matches would inevitably increase the scrutiny on Arbeloa.
For now, the Spaniard is refusing to be distracted by questions about his future. His message is that the work on the training ground, confidence in his players and the need to start collecting points must take precedence over speculation about his job.