Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
Blackpool have signed Rochdale full-back Tom Kennedy on loan, while Tangerines striker Francois Zoko has joined Bradford.
The Spain international has been linked with a return to his home country, with Atletico Madrid believed to be prepared to launch a bid for him.
Atletico coach Diego Simeone has not denied that his side were interested in Cazorla, who joined the Gunners last summer from Malaga for £15million, commenting last week that "anything is possible" when asked about the midfielder.
However, the 28-year-old, who is enjoying the final days of his extended summer holiday before joining up with his club for pre-season training, has reaffirmed his commitment to Arsene Wenger's side.
He told reporters: "There has been a lot of speculation about a move to Atletico Madrid but I'm very happy at Arsenal, I have a contract there and I start training on Monday.
"Perhaps I will return to Spain one day, but right now it's very unlikely," he added.
Atletico's most significant signings this summer have been Leo Baptistao, who joined for around 7m euros (£6m) from Rayo Vallecano, and David Villa, who arrived from Barcelona for an initial 2.1m euros (£1.8m).
Although Cazorla stressed he was not about to link up with his Spain team-mate Villa at the Calderon, he said he was pleased for him.
"I'm very happy for Villa, because he had a difficult year with Barcelona due to his injury [a broken leg he suffered in December 2011], but now he's got another chance to shine again," he said.
And he declared to work extra hard this year for Arsenal so he can be guaranteed a place in Spain's squad for next year's World Cup in Brazil, after missing his country's triumph in South Africa due to a back injury.
He said: "I still have unfinished business in the World Cup after missing the last one because of my back. I really want to experience a World Cup, so I have to have a great year with Arsenal. I hope this year is even better than the last."