Manager Archibald has guided the Jags to finishes of 10th, ninth and eighth over the last three campaigns.
"On and off the pitch, he's had a big influence," striker Doolan told BBC Scotland.
"It's no surprise that people are taking notice of that and hopefully we can keep hold of him."
Archibald is no longer on the short-list for the managerial vacancy at English League One outfit Shrewsbury and Doolan is pleased the 38-year-old decided he had "unfinished business" at Firhill.
"Alan is a massive figure round the club and he symbolises all that's good about Partick Thistle," he said.
"He's built something here that's long-lasting."
Doolan is unconcerned about his own lack of league goals so far this season.
The 29-year-old scored against Airdrieonians in the Scottish League Cup in August, but none have followed in the Premiership.
"I'm there to score goals and that's what I've done year in, year out," said Doolan.
"You pull on your experience from years gone past and there have always been times when you haven't scored - it's nothing to panic about."
Doolan's strike-rate has reached double figures in each of his last six years at Firhill.
The former Auchinleck Talbot man had only scored twice at this stage last season but went on to net another 12 before the end of the 2015-16 campaign.
Thistle are still waiting on their first Premiership win since beating Inverness Caledonian Thistle on the opening day of the league season.
In what is their fourth consecutive season in the top flight, the Maryhill men are 11th in the Premiership - level on six points with bottom club Dundee - but Doolan feels it is far too early to read anything into that position.
"Look at the league table; it's so tight," he said ahead of the weekend game with Ross County.
"One win and the full outlook of the season can change, so we're going into Saturday with high hopes.
"We've set standards across the years that we've been in the Premier League and it's up to us to maintain those standards and surpass them.
"It's testament to the club that now we're not considered the yo-yo team."

The 1-0 win, courtesy of Nicky Cadden's penalty, kept Livi a point clear of Airdrieonians, who have a game in hand and beat Peterhead 4-2 away.
Queen's Park moved above Albion Rovers into fifth place by beating Brechin.
The Spiders, who won 2-0, are now five points behind third-placed Brechin, with Alloa, who are fourth, inactive.
The Wasps, like Stranraer, East Fife and Stenhousemuir, were not in league action, though Stenny beat Forres Mechanics in the Scottish Cup.
At Cliftonhill, Ross Dunlop fouled Dale Carrick in the box and Cadden converted the spot-kick in the penultimate minute.
There was further misery for the hosts as Alan Reid was sent off in stoppage time following his second booking.
Airdrie raced into a three-goal lead at Balmoor with Andy Ryan's strike, Sean McIntosh's header and Iain Russell's finish all coming within the opening 20 minutes.
Nicky Riley replied for the hosts before half-time and Leighton McIntosh's penalty following Jack Leitch's foul on Riley further reduced Peterhead's arrears.
But Ryan's second effort of the match deep into stoppage time clinched the visitors' win.
Brechin City lost ground on the top two after losing at Hampden.
Ross Millen opened the scoring from the penalty spot after a first-half foul by goalkeeper Graeme Smith on Dario Zanatta and Ryan McGeever headed home a late Sean Burns corner.
Kris Doolan has stressed the importance to Partick Thistle of holding on to Alan Archibald after a failed approach from English club Shrewsbury Town.
[NEXT_CONCEPT]
Livingston maintained their slender advantage at the top of Scottish League One with a narrow and late victory over Albion Rovers.