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."
Meanwhile, Lennon admitted hopes were fading that defender Lee Mair would recover from a stomach muscle injury in time to make the final.
Mair picked up the injury in last Wednesday's defeat by Dundee and missed the weekend draw with Dundee United.
Lennon said: "It's looking more unlikely than likely.
"I don't want to build the boy's hopes up and it comes flat. It's not looking good.
"Lee is toiling and will see a specialist tomorrow.
"While it's a massive game, and cup finals for clubs our size are far and few between, and my heart goes out to the boy, that's part and parcel of football.
"But what's equally important is we have nine very important games after the final and we have to make sure we use the squad entirely.
"I'm very disappointed for him."
Meanwhile, Dundee United have confirmed they will not submit an appeal against John Rankin's red card at St Mirren Park.
The midfielder was shown a straight red by John Beaton for a two-footed tackle on John McGinn towards the end of the goalless Clydesdale Bank Premier League clash on Saturday.
Rankin appeared hopeful of having the card overturned when he appeared on BBC Scotland's Sportscene last night but United have decided against launching an appeal.
The 29-year-old will now sit out Sunday's SPL derby against Dundee at Tannadice through suspension. Fellow midfielder Willo Flood is also suspended.
Rankin had told Sportscene: "When you look at it again, I don't think it's so bad.
"There's no malice in the challenge whatsoever and hopefully we'll overcome the appeal later in the week.
"I've read it, but none of my two feet are off the ground. I've tried to keep both of them on the ground and my studs aren't showing.
"The referee is right on top of it and he's got to make a split decision, but I think he's a bit quick with the cards."
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