The 24-year-old revealed he has settled in quickly and is looking forward to regular first-team football, but Paul Lambert indicated a summer transfer may prove too costly
The 24-year-old arrived at Villa Park earlier this month after failing to hold down a regular place under Blues boss Jose Mourinho, who preferred Ashley Cole and Cesar Azpilicueta at left-back, and made his debut in the 2-2 draw at Liverpool.
Bertrand will make his first home appearance in Wednesday's West Midlands derby against West Brom, but stresses it is too soon to speculate over his long-term future.
"I'm just here to concentrate on each game as it comes and to get back playing regularly," he is quoted as saying by The Birmingham Mail. "I'll leave all that stuff until the end of the season.
"You can't rule anything out. It's important, first and foremost, that my performances are good enough. I need to concentrate on each game.
"I've settled in quite easily. It's fortunate, to be fair, because I know half the team through England at younger ages. It has been good. It's great to be involved in a derby for my first home game."
Villa boss Paul Lambert remarked that even if he was interested in making Bertrand's move permanent at the end of the season, the cost could prove a stumbling block.
"He's Chelsea's player and we're thankful to them for letting him come here," he added. "What Ryan's value is I haven't a clue. He's played in the biggest club competition [the Champions League] and won it so he knows how to do it.
"That's the main thing, the value of him. If you are buying him you're not buying a novice, you're buying someone who has won the European Cup and I'm pretty sure they won't come cheap."