Tottenham were linked with a number of left-backs during the transfer window, with the club allowing Benoit Assou-Ekotto to join Queens Park Rangers on loan.
Rose, who enjoyed a successful spell on loan at Sunderland last season, is determined to grab his chance in the Tottenham starting XI after starting all three games so far in the Premier League this term.
Having failed to bring in any new left-backs, Rose is set to remain as first-choice in that position - and the England Under 21 international is happy he has the backing of Villas-Boas.
"I spoke to the manager about the left-back situation and he assured me that if he still wanted a change, he'd come to speak to me first, which is great," Rose told the London Evening Standard.
"I wasn't looking to go anywhere just yet. I'm enjoying the run in the team and long may it continue."
Tottenham have been tipped as potential title contenders following their impressive business in the transfer window, but Rose admits their aim is to finish in the top four.
"You look through the whole team and you see that you've got two strong players in each position and it's great," added Rose. "We've got a very good squad.
"We've given ourselves a good platform and we'll take it from there, although it's too early to guess where we might finish. The aim is to finish in the top four."