The 24-year-old, who is a free agent after leaving Finnish club KuPS, has been training with Saints after failing to win a deal with Kilmarnock.
And Lennon revealed he would make a decision on the 47-times capped player before Sunday's Hampden clash with Hearts.
Lennon said: "We have had Sander in training and we will monitor him very closely.
"We are always interested in good quality players and he certainly comes with that pedigree and has a CV to back it up.
"We like what we see so it's looking promising.
"Not just us, but it also gives him the opportunity to get a feel for our football club and make sure it's right. I wouldn't envisage a problem with that.
"We will monitor it in the next two or three days and then we will make a decision."