The 20-year-old, the younger brother of Motherwell star Henri Anier, joined the SPFL Premiership newcomers last week and will spend the coming days training with Archibald's squad as he bids to win a deal at Firhill.
Thistle's League Cup-tie with Dundee United last Wednesday meant Anier's chances to impress were limited during his first week with the club, but boss Archibald is keen to see him in action, with the former Flora Tallinn and Odense Boldklub forward set to appear in a behind-closed-doors fixture later this week.
Archibald remains on the lookout for another forward to add to his squad to provide competition for main strikers Kris Doolan and John Baird, but Portuguese attacker Rui Ferreira will not be offered a deal at Firhill following his trial spell.
A lack of cutting edge has proven costly for Thistle in the opening weeks, with the champions winning rave reviews for their free-flowing style yet unable to turn their impressive attacking play into enough goals, or wins, thus far.
Doolan netted his second top-flight goal of the season with the opener in Saturday's 1-1 draw with St Johnstone, while Baird has yet to find the net since making the move from Dundee.
Archibald's other summer striker signing, Liverpool loan youngster Henoc Mukendi, has struggled to break into the first team in recent weeks, with Anier now set to be put through his paces once again as the Jags boss looks to add a different dimension to his forward line.
Thursday's bounce game could also see defender Jordan McMillan make his latest return to action after a frustrating start to the campaign.
The former Rangers and Dunfermline star has yet to feature for Archibald's side this term after picking up an ankle knock during pre-season and suffered a setback in training a fortnight ago.