The Gorgie side are sitting comfortably third in the Ladbrokes Premiership with 50 points from 27 games following their return to the top-flight and the former Jambos defender has second-placed Aberdeen in his sights.
To that end, Neilson is looking to build on victories over Kilmarnock last weekend and Inverness on Tuesday night when seventh-placed Jags visit.
He said: “We knew we had a big week this week with three home games.
“We have managed to win two and we want to make it three out of three.
“But Thistle are a team pushing for a top six, they are a tough team with some good players.
“I think Alan Archibald has done a great job. I know him quite well, he got them promoted, got them stable and now they are in a position where they are thinking about the top six.
“But if we can get the result on Saturday it guarantees top six for us.
“It was what we set out for at the start of the season so it would be great if we could do that and then it gives us a chance to focus on getting up the league.
“You look at your target and try to get it and once you get it then look at the next one.
“It is important that we don’t get carried away. You have to respect the teams you are playing against.”
Neilson revealed that midfielder Perry Kitchen should start his Hearts career next week.
A work permit for a two-and-a-half year deal has been secured for the 24-year-old USA midfielder, a free agent after leaving Major League Soccer team DC United, and he has returned to America to finalise paperwork.
“I was pleased to get him and quite surprised,” said the Gorgie boss.
“ He had a big offer in the MLS but he wanted to come to Europe and play to progress himself to get into the international team more consistently.
“He had an offer from a German team which fell through at the last moment and because it was February he couldn’t make a move there because their window shuts.
“But we can still bring in free agents and it was a chance to get him in.
“He is a defensive midfield player who sits in front of the back four, he’s very mobile, athletic and a good player.
“He has played in the US national team which is a really good level.
“It is just paperwork. We got the permit agreed last week and he has got to go back to America to pick up the forms but he should be in training next week.”
Neilson confirmed that right-back Callum Paterson will be out for a month with a shoulder ligament injury sustained last week against Killie.
He said: “He went over on it but it felt a lot better and we were hopeful he had jarred it.
“But the scan showed a little tear so it is important to let it settle down.
“He has been one of the key players but we have a squad and strength in depth.”
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