Former Dundee United midfielder Mark Kerr is set to be offered a contract after scoring a 30-yard effort in Saturday's 4-3 friendly win at Dumbarton, which also featured another Thistle trialist.
Archibald is also aiming to sign Gary Fraser on loan after the 19-year-old midfielder joined Bolton from Hamilton.
"I've got until the end of August to try and get things sorted but I really want to get things sorted as quickly as possible," he told his club's official website.
"We are always on the lookout for players and it wouldn't be a surprise if there were a couple of more trialists in Tuesday's game with Livingston."
Archibald is looking to strengthen in central defence and was encouraged by his latest unnamed trialist.
"I thought the lad did well," he said. "I thought he acquitted himself well. He hasn't had any pre-season and he only arrived late on Thursday and he only had one training session with us."
Archibald added: "We're speaking to Bolton about bringing Gary Fraser in on loan and we are probably going to offer Mark Kerr a contract.
"He's done really well and he is the right type to come in and enhance our midfield. We had a bit of an injury crisis in midfield towards the end of last season and that left us a bit short and it is an area that we need to be well covered in.
"So we will offer Mark something and we will see where things take us with Gary Fraser."