Set to be replaced alongside Daniel Ricciardo at Renault next season, Hulkenberg is without a drive for 2020.
Both Williams and Alfa Romeo have seats available, though the Ferrari-backed Antonio Giovinazzi has first call on the available Alfa drive and Nicholas Latifi looks likely to step into the Williams driver alongside George Russell.
Red Bull has yet to confirm its full driver lineup, though there seems little appetite to deviate from the current fleet of drivers under its employ.
It poses the very real prospect of the German leaving the sport at year's end.
“It doesn't feel like unfinished business,” Hulkenberg said of his time in F1.
“I've done my business, I've really performed well over the years, very consistently, many times when it was on the verge when other people didn't get hired or get a job, I still was wanted, and paid to drive.
“That also speaks for some quality. Of course I would like to have a different kind of record, more points, a podium and victories.
“I know the reasons why things maybe didn't go that way but I'm at peace with myself there, I sleep well at night with my eyes closed.”
Hulkenberg has long been touted as a star of the sport after an immensely successful junior career that saw him win the A1GP title in 2006-07, the 2008 Formula 3 Euro series, and 2009 GP2 Series.
The German made his F1 debut with Williams in 2010 and spent 2011 testing for Force India before joining the team as race driver the following year.
A switch to Sauber followed before rejoining Force India for 2014 and ultimately finding his way to Renault for 2017.
A 24 Hours of Le Mans winner with Porsche, driving with Earl Bamber and Nick Tandy to take the French classic in 2015, the 32-year-old says he's in no rush to jump into another series simply to compete.
“I don't want to rush into something or jump into something just to race,” he said.
“It needs to be something that I like, a challenge that excites me. I have no conclusion, no perfect answer for that yet.”
At season's end Hulkenberg's F1 record will include 179 grands prix with 177 starts, but is yet to stand on the podium.
He claimed pole position for the 2010 Brazilian Grand Prix, while his best race result is fourth (Belgium 2012 and 2016, and Korea 2013).