Her team believe the SNP Shadow would collaborate more with Holyrood, and is "above the divisive issues" that have previously caused spats within the party.
She is running against Stephen Flynn, the MP for Aberdeen South, who announced plans to stand last week.
It comes as Ms Thewliss nominated Stuart McDonald MP to be deputy, following the announcement Ian Blackford would stand down last week.
His deputy, Kirsten Oswald, also said she would step away from her role at the party’s AGM.
A source close to Ms Thewliss’s campaign told The Scotsman her appointment would bring about “smarter collaboration” across the SNP.
They said: “There would be a focus on teamwork, bringing out the best of the group in Westminster.
"It would be helping to work with colleagues in other parts of the party, whether that’s headquarters, the Scottish government or the party at large.
“There has been a suggestion remote control from Edinburgh is a problem, the idea Westminster needs to be free from HQ, and that is wrong.”
The source also insisted Ms Thewliss was not “continuity Blackford”, but insisted they were against his resignation.
They said: “She is not continuity Blackford, she is very much her own woman who charts her own course, and that is about teamwork and collaboration.
“None of us favoured Ian resigning, we think it’s an act of madness.
“He is one of the few politicians to have a net approval rating, and when he resigned his approval rating went up by 13 point.
"The party adores him, and you can see that when he goes on stage or does events.”
Monday also saw the MP for Cumbernauld, Kilsyth & Kirkintilloch East throw his hat in the ring on Monday morning, announcing he would stand to be second in command, after a nomination from Ms Thewliss.
In a statement posted to Twitter on Monday, Mr McDonald said: “The party is at such an important point in its history.
“Our mission is to actively build and make the case for a progressive alternative to Tory austerity and Brexit – Scotland’s independence in Europe.
“As deputy leader of the group, I’ll work with Alison to build a strong, focused Westminster team that works in collaboration with colleagues from across the party.
“We’ve got a big job ahead. Let’s get it done.”
Aberdeen South MP Mr Flynn has not officially announced who his pick for deputy would be.