Kljestan has made 11 appearances for the US national side
Gordon Strachan and his Celtic backroom team will decide whether to pursue their interest in USA midfielder Sacha Kljestan within 24 hours.
The manager said he was working hard to make signings before the closure of the January transfer window.
But he said: "If we don't bring anybody in between now and next week, I don't have a problem.
"Because, although it will be hard, I feel that I can deal with the players here to win another championship."
Kljestan, who plays for California-based Chivas, has spent a week training at Celtic's Lennoxtown complex.
He scored five goals from 22 matches in the last Major League Soccer season and was named US Soccer's Young Male Athlete of the Year.
Kljestan also played at the Beijing Olympics, where he scored twice in three games.
You usually find that most of the action happens in the last three or four days of the transfer window
Celtic manager Gordon Strachan
He has been capped 11 times since his 2007 international debut, including four World Cup qualifiers in 2008, and is scheduled to return home in time for the USA's friendly with Sweden on 24 January.
Strachan stressed that Celtic's lack of transfer activity during January was nothing to do with title rivals Rangers being unlikely participants themselves because of financial problems.
"It's been shown over the years that the signings at this time have been beneficial to the club," he said.
"But you usually find that most of the action happens in the last three or four days."
Celtic's lead over their city rivals at the top of the Scottish Premier League was reduced to two points after Strachan's side lost 4-2 to Aberdeen last weekend.
But Strachan was shrugging it off as just one of those games when everything went right for the underdogs.
"They had four attempts to score and scored four," he said.
"We had 20 attempts at goal and scored two. We scored five there last year with 13 attempts on goal.
"After 22 games, we are at the top of the pile. We are still in the CIS Cup and the Scottish Cup.
"That's the healthiest it has been since I came here as usually we are out of one cup or another."
Aberdeen's goals on Sunday came from set-pieces, but Strachan was not overly concerned.
"Before that, there's only one team that scored from a free-kick against us," he pointed out.
Bookmark with:
What are these?