The 25-year-old goalkeeper has been heavily linked with a move away from the Britannia Stadium after another standout season for the Potters in 2012/13.
Gunners boss Arsene Wenger has been credited with an interest in bringing Begovic to the Emirates Stadium as he looks to increase competition for a first-team place for the likes of Wojciech Szczesny and Lukasz Fabianski in north London.
However, Arsenal will face serious competition for the player's signature, with Liverpool ready to lodge a rival bid to lure Begovic to Anfield, as Pepe Reina's Merseyside future continues to be shrouded in doubt.
Manchester United complete the trio of Premier League parties believed to be monitoring the Stoke stopper's situation, though it was Sir Alex Ferguson - and not David Moyes - who was rumoured to be considering an offer to tempt Begovic to Old Trafford.
"Now, I'm on my way for a holiday, but I don't know yet what will happen," reflected the in-demand goalkeeper in an interview with SportSport.
"Will I leave Stoke City? There are many rumours, but so far I didn't get any concrete offers. But that doesn't mean that I will not get one."
The recent departure of Tony Pulis has also fuelled speculation that a number of first-team stars could leave Stoke this summer. But, Begovic insists he is paying little attention to transfer tittle-tattle and is instead focusing on preparing for the upcoming World Cup qualifiers with Bosnia-Herzegovina next month.
"Right now, I don't want to think about all that," he added. "First, I need some days off, then I have an important match with my national team."