Martin O'Neill insists Celtic are "working hard" to add to the squad and believes new signings are "relatively close."
Only right-back Julian Araujo has joined the Parkhead club on loan so far this month, with a striker remaining top of the wanted list.
Fans are becoming agitated at the lack of transfer activity with the Hoops currently sitting third in the Scottish Premiership, but O'Neill is confident of strengthening this month.
"I'd love to blame other people, but it's down to me," he said ahead of Wednesday's league trip to Falkirk.
"The January transfer window is pretty difficult because unless you've identified a player that you absolutely know is going to improve your team and that you're prepared to spend the money on him.
"We are genuinely working really hard in the background, so there's no impediment in that sense. It's just trying to get some people in that we think could help us now, at least until the end of the season."
Asked if he had been offered potential signings, O'Neill added: "That is true, yes, and I have discarded some.
"We are, I know, famous last words, but we are making progress, or we think we are.
"But you're talking about agreements with clubs, you're talking about if that's the case for a start, number one, and then secondly with players themselves, and then people finding out that, or players finding out that there's interest elsewhere.
"So you're competing, all those particular things come into consideration, which is no surprise to me.
"I know you're thinking, we're halfway through January now, but I think that we're relatively close.
Jota set to miss entire campaign
O'Neill also revealed Celtic are unlikely to have Jota available at all this season.
The 26-year-old winger has been out since suffering a serious knee injury against Dundee United in April last year.
It had been hoped he would return in February to help the Hoops in the title run-in.
"Obviously, I'd like to bolster the squad," the Northern Irishman added.
"I don't see, for instance, in terms of the long-term injuries, I don't see Jota being back this season.
"I think that Alistair Johnston would probably make a fight back, and he's hoping to be maybe sometime in March, and that would be great if that's the case.
"But the longer-term injuries, I don't see it."
Celtic have recalled centre-back Stephen Welsh from his loan at Motherwell.
With Cameron Carter-Vickers still out injured, O'Neill wanted cover for Auston Trusty and Liam Scales.
Welsh has impressed at Fir Park, but the interim boss insisted they had no choice.
"Number one, he's our player. So that means something," the former Leicester manager added.
"He's having a really great time at Motherwell, and I understand from a playing viewpoint that having got himself up and running, he might not have wanted that disturbed.
"There was a cut-off point where we could take him back and then send him back to Motherwell. That might happen."
