Celtic have offered a contract to Brad Guzan, the Chivas USA goalkeeper who has trained with the club this week. The 23-year-old has impressed the Celtic coaching team and Strachan views him as an exciting long-term prospect.

The manager is still weighing up a move for Seweryn Gancarczyk, the 26-year-old Polish left-back who has also been on trial this week.

"Brad is away back to think about it and I'll speak to Seweryn later on today,"

said Strachan. "Peter Lawwell, the Celtic chief executive has made Brad an offer. We're thinking more about buying people we can invest in for the future rather than spend for now and it's dead money. Our team has become a lot younger in the past couple of years and if we think it's good value for years then we'll do it."

Strachan confirmed the club have not received, and are not encouraging, any offers for Lee Naylor, who has been linked with a move to Portsmouth. Celtic have received an enquiry from Burnley from Derek Riordan but will retain the former Hibernian striker's services until they receive an appropriate bid.

Asked if Riordan would still be at Celtic come the close of the transfer window, Strachan said: "I have no idea. I showed last week when we had a crisis in the first 20 minutes, I put Derek on. I think that answers a lot of what I think about him. There's been a lot of good competition for places. If you think of our wide players, Shaun Maloney and Nakamura - and Derek likes playing these positions - have both been Scottish player of the year. And you could argue the best and most exciting player of this year has been Aiden McGeady. He's been very unfortunate. You can't plan for that when you're signing players. "

"We'd be quite happy if the squad was the same size. You like to try and improve your squad but it is to get players that are better than we've got. To guarantee that you would have to spend £15-20m and it is not going to happen."

Celtic have a tough fixture schedule ahead with three away games, against Falkirk on Sunday, Motherwell and then Aberdeen. Strachan stressed the importance of picking up maximum points, with his side now trailing Rangers by four.

"It's a stretch we look at and think the pitches aren't great just now so we just have to churn out results. If you're dropping points at this time of the year, whether you're in the lead or second, then they're crucial."

An injury to new signing Andreas Hinkel could mean Paul Caddis starts at right-back against Falkirk tomorrow, though Jan Vennegoor of Hesselink is a doubt after picking up a head injury last weekend. Celtic have rediscovered some form in recent weeks with four wins on the trot and Strachan declared himself reasonably happy with the progress of team three'.

"You are judged on winning things so we will see if this team goes on from here. They either become very successful or we have a blip and have to deal with that. I can't be sidelined from what I am trying to do by immediate results."