McCall revealed he would press ahead with talks with chief executive Leeann Dempster in the "next week or so" in a bid to ensure both players extend their deals beyond the first half of January.
Estonia striker Anier has scored five goals in 19 games since joining from Viking Stavanger while Rotherham winger Ainsworth has made five starts and five substitute appearances in an injury-disrupted spell.
McCall, who is looking for his first home win over St Mirren as Motherwell manager on Saturday, said: "We will be in discussions about those two boys. Both of their agents have (indicated they want to stay) and I'm sure they are enjoying themselves.
"We will have to have a look at a couple of things but all being okay it would be nice to get them signed up until the end of the season.
"We will be hopeful, I have not really sat down with Leeann, obviously it's a busy period, but there are tentative enquiries."
McCall admitted he feared it might not be possible to keep the players after Motherwell's William Hill Scottish Cup defeat by Albion Rovers hit their finances.
"Of course and it still might not be," he said. "We just have to see. If we don't manage to keep Lionel or Henri, if we could get another face in then it would be great."
Motherwell are looking for their 10th Scottish Premiership win of the season when the Paisley side visit Fir Park.
And defender Stephen McManus admitted he was shocked to hear McCall's side are four points better off this season than they were at the same stage last term.
Motherwell comfortably finished second but were fifth at this stage last year, the same position they occupy now, albeit they were a point behind leaders Celtic.
McManus, who joined from Middlesbrough in the summer, said: "I feel this season we have been a bit stop-start, we have not really got into a rhythm. We are winning one, losing one, drawing one. So it would be nice to go on a wee bit of a run.
"It's all right saying you are going to get into a rhythm but we need to put it into practice.
"The manager told us a stat a couple of weeks ago saying we are four or five points better than off than we were last year, which I was shocked at to be honest, because every time I watched Motherwell last year they were always winning.
"I feel there is a bit more to come. Everybody seems to be talking about Aberdeen and Dundee United and how well they have been going this year, which they are quite right to do so, but then you look at the table and we are only one point behind them.
"I think it's important that we are not being too hard on ourselves because there is always expectancy levels on the better clubs in the league but you still need to have reality check as well. We are not going to go on a 10-game winning streak the way Celtic can do.
"We have not done too badly so far but I think there is more to come."