Forward Doolan yesterday launched the Jags' new home kit for their second campaign in the SPFL Premiership.
Doolan and Taylor were instrumental in Thistle's battle to beat the drop last term as Alan Archibald's side ensured they would play top flight football once again this year.
The former Falkirk star has returned to parent club Sheffield United after his Firhill loan came to an end, with Thistle battling it out with the Bairns for his signature this summer.
Doolan said: "Of course I would like to see Lyle coming back next year.
"He was a great help to us when he came in and scored a few goals for us.
"I would be delighted to see him coming back. It would be a massive signing for us.
"He is a Sheffield United player just now and it is out of our hands.
"Until he becomes a Partick Thistle player there is not much we can do about it.
"But, if he came back, I would be delighted to see him.
"I haven't heard from him all summer to be honest. I have kept quiet and just relaxed."
After a well-deserved summer break, the Thistle squad will return to action this week as boss Archibald gets set to put his squad through their paces.
The Jags will head to Spain for a week-long training camp before returning to Scotland for their first friendly clash with Championship side Dumbarton.
They will kick-off their second Premiership campaign at home to Ross County on August 13.
It was a season to remember as the Jags secured their top flight safety with a game to spare by beating Hearts.
And Doolan is determined to shine even brighter on the big stage next season. He said: "To lose Hearts and Hibs is a big thing, it is a big loss to the Premiership. But we can only look after ourselves.
"We have got a great fanbase at the club and we are looking to push on and cement our place in this league now.
"If we progress the way we have been, and with the players we have got and who will potentially come in, I see no reason why we won't do that.
"It would be brilliant to finish in the top six. If you gave us that now we would take it.
"That is always something to aim for. It is important there are high aims at the start of the season.
"If we could get into the top six, that would be brilliant for the club."