but don't expect to see either man becoming a regular starter for the Hoops any time soon.
That's got nothing to do with the fact the club are trying everything they can to acquire another striker before the window closes tonight.
They could be unsuccessful in that chase, but it still wouldn't open the door to Teemu and Amido.
They are 'victims' of the run Celtic are on - and the fact Neil Lennon wants to keep it going for as long as possible.
Their consistency, in terms of securing comfortable victories and clean sheets means Neil is sticking by the same format and players.
The frontline combination of Anthony Stokes and Kris Commons was working very well up until the former got himself suspended.
Now that Anthony is available again, look for an automatic return to the starting XI. That might seem a bit harsh on Teemu and Amido, who clearly need game time.
But, remaining unbeaten and extending records is what is driving the team at the moment.
And, while this continues, the Bhoys on the outside will continue to be left looking in, with all of the frustration that will bring.
If and when the run does come to an end, Neil will look at it again. He might find that the removal of this goal for the players means the team needs freshened up.
That's one of the reasons he, along with chief executive Peter Lawwell, has been working so hard for the past four weeks to bring in new players.
It is a very tough time for Neil trying to manage the team and expectation from the supporters who are checking the websites every other minute to see if they have signed anyone.
Of course, even if you do manage to find a player at the right price and asking for manageable wages, there is never any guarantee he will prove value for money.
Every signing is a gamble, and, the lower down the price range you are shopping, the greater this gamble tends to be.
Neil has already made it clear Mo Bangura is not going to figure in his plans. But, telling a player he has no future at the club, and actually getting him out of the door are two very different things.
Will anyone want to buy him? He cost Celtic over £2million, but what is his value now?
I don't expect Mo or his advisors will be keen to see him simply end his contract - which is due to run through to next year - and walk away without being paid up.
And I don't imagine for one minute Celtic will be eager to fork out even more money on a guy who has barely shown any return for the investment already made in him.
It's not an unusual situation in football, and every manager has made signings which simply have not worked out.
The important thing is to accept the situation and try to end it as quickly and inexpensively as possible.
It is too early to make any decision on Teemu or Amido.
While Teemu has started many more games than Amido, neither man has really had enough time on the pitch to allow us to make a definitive judgement on them.
More often than not they have come on as subs. Sometimes this has been for as little as five or 10 minutes.
With strikers in particular, they need to be on the park to find their sharpness and best form. But, as I said earlier, Neil is sticking to a tried and trusted line-up. And, when you look at the results, who can argue with him?
Anthony and Kris have worked hard to develop a good partnership up front - as the number of goals the team has been scoring confirms.
Okay, Anthony has not found the net as often as he has done in previous seasons, but Kris has more than surpassed his best strike rate - and a lot of that is down to how Anthony combines with him.
They do not have a big physical presence. But, traditionally, Celtic's goal threat has not come from a big striker. Think about the likes of Kenny Dalglish, Bobby Lennox, Dixie Deans, Lou Macari. The list goes on.
The exception to this was when Martin O'Neill brought in Chris Sutton and John Hartson. But, even then, Henrik Larsson - who had a magnificent leap, but was not the tallest - was the main goalscorer.
It's about how many you score, not how big you are. So, it really should have been no surprise when Neil turned his attention to Leigh Griffiths.
I have known him since he was a teenager at Livingston, and I always found him to be a likeable lad with real ability.
I can understand why Neil considers he would be an asset to the squad, and a player with scope to improve.
At the price Celtic are prepared to pay, Leigh would be a speculative signing.
But, then, most players are.