The Frenchman signed for the north Londoners on transfer deadline day but was initially benched by manager Andre Villas-Boas with Brad Friedel in fine form.
However, having started in Sunday's 2-0 win over Aston Villa, the former Lyon keeper has reiterated that he has no problems with his start to life in north London.
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"We have to put things into perspective. I just spent a month with Spurs, I arrived during the season with a team in place and I have only missed three games," Lloris told reporters.
"Against Manchester United, I wanted to be on the pitch. Things are clear, I have not signed for Tottenham for this role.
"I think it will happen naturally. I am in the service of the team, I respect everyone, I came to play but I have no guarantee. The coach will make his choice."
Lloris' starting role against Villa brought to an end to Friedel's run of 310 consecutive Premier League games, but the 25-year-old believes competition should be expected at a club like Spurs.
"I talked with the coach, there was no ambiguity. He told me that everyone wanted I come to Tottenham and England," he added.
"Only the manager has some control over these things. But I can not control what is written. Compared to what is said and what I hear, everything is going very well.
"There are four high quality goalkeepers here, and choices are made by the coach, I have just been recruited as part of a future project, but the project of the future starts now.
"Competition exists everywhere, but relations with Brad Friedel, with goalkeeping coach [Tony Parks] and manager are good.
"After that, it is not me who manages the communication. I'm back, I'm training and I am happy to play."