It was expected that the Mexico international would be among those offloaded by Spurs this summer as they usher in a new era under Andre Villas-Boas.
Dos Santos has struggled for games throughout his time in England and has taken in regular loan spells as a result.
A permanent switch would be beneficial to all concerned, but the 23-year-old says he will continue to fight for a first-team role if he remains in north London.
"The window closes at the end of August and I am calm, I'm not getting desperate," Dos Santos told Record.
"I'm still a Tottenham player and if there is no other option, I'll stay and do my best like I have always done.
"I can't complain. I have learnt a lot at Tottenham, the team have great quality, and it won't be a bad thing if I have to stay."
Reports have suggested that La Liga outfit Malaga are keen to take the former Barcelona playmaker back to Spain, but Dos Santos claims no official approach has been made.
"Nothing concrete has come as yet, we expect that will happen within the next few days," he said.
"I'm very relaxed here with the national team (at a pre-Olympic training camp), my head is here and my agent is dealing with everything.
Dos Santos added: "I am trying to keep myself away from it all and focus here, to be 100 per cent and not get worried about the clubs.
"There are obviously options, but I'm relaxed. I talk to my agent every day and he has told me to stay calm and that there will be news soon."