The council is using global recruitment company Berwick Partners to find its fourth new chief executive in three years.
It comes as a leaked report has cast doubt on the credibility of a corruption inquiry that has dogged the council for more than five years.
Berwick Partners, part of Odgers Berndtson, describes itself as "an agile, proactive executive search and recruitment firm, with offices in the US and throughout the world" on its website and could charge in the region of £20,000 for its services.
Its advert for the role offers a salary of around £185,000 plus "package". Berwick is also advertising the chief executive job at the West Midlands Combined Authority, working alongside Mayor Andy Street, with a salary of around £190,000.
The job advert for the Sandwell role said: "It’s a busy and demanding time here at Sandwell Council.
"With a new Council Leader and a recently revitalised senior leadership team, we are now seeking an exceptional Chief Executive to make things happen and to truly put Sandwell firmly on the map."
For the last 10 years the council has been mired in a string of scandals, inquiries, investigations and resignations involving former deputy leader Mahboob Hussain and other former leading Labour politicians.
The advert continued: "Described as a sleeping giant, Sandwell is one of the largest boroughs in the West Midlands with over a third of a million residents. Like any large metropolitan borough, Sandwell faces many challenges, but also has an impressive number of opportunities to build on over the next five years.
"These include the new Midland Metropolitan University Hospital, the new Sandwell Aquatics Centre (hosting the swimming and diving events for the 2022 Commonwealth Games), the extension to the Midland Metro line, HS2, and a £67.5m Town Fund allocation.
"Our ‘Big Plans for a Great Place’ strategy is simple but ambitious in its intent: clearly focused on a borough where people are proud of their local area, have better paid jobs, increased levels of skills, and more opportunities."
The council wants the new chief executive to be at home operating on the national political stage and ensure the borough's 330,000 residents get value for money for their taxes.
The advert said: "Our new Chief Executive will need to be highly skilled and experienced. Our aspirations are high, but so are our expectations.
"We need a leader with a strong, strategic mind who is a clear thinker. Someone who understands and has an organisational grip of the competing demands of service delivery, organisational performance, and partnership working.
"Someone who is adept at negotiating the politics at regional and national levels and creating opportunities for Sandwell make a strong contribution to the West Midlands Combined Authority; and someone who will raise the profile of Sandwell nationally and internationally."
The new chief executive will take over from Kim Bromley-Derry CBE DL who was the interim boss after replacing David Stevens, who stood down after 18 months in charge. His salary was £147,000 which means to entice the right candidate this time the council has added another £38,000 to the chief executive's wage.
Stevens' predecessor was Jan Britton who ran the council for eight years before resigning after a series of rows with his political bosses.
Current council leader Rajbir Singh is the sixth leader since Councillor Darren Cooper's sudden death in 2016 due to regular infighting in the controlling Labour group.
If you think you are the right man or woman for job then phone Jonathan Clark at Berwick Partners on 07736 818185.
A Sandwell Council spokesman said: "This is an important post for Sandwell to recruit to, going forwards.
“Our HR service are working jointly with a recruitment consultancy called Odgers. They have been appointed to assist us with the recruitment as they are a well-respected and established executive search agency who specialise in recruiting to crucial senior management roles across the public sectors.
“This is common practice for most chief officer posts in the public sectors."
The Council refused to be drawn on the cost of the consultancy fees, saying it is commercially sensitive information.