Willock, 21, became the youngest player to achieve the feat as Newcastle moved provisionally up to 15th in the standings after their final home game of the season.
The Arsenal loanee scored in first-half stoppage time when he made a run into the box and leapt to head home Jacob Murphy's cross, prompting Newcastle fans to chant "Joe Willock, we want you to stay" after the game.
"I'm not sure [about my future]. I need to have a conversation and see what the best move for me is," Willock told the BBC.
"I have made friends for life and made a really big connection with the fans. It is one of my options and I am going to consider it."
Newcastle manager Steve Bruce said keeping Willock at the club was a difficult decision.
"We have to respect he's Arsenal's player," Bruce said. "If we can, we'd love to bring him here... he's exactly what we needed."
Jonjo Shelvey also came close to scoring in the first half for Newcastle with a powerful header from point-blank range. only for his effort produce a fine reaction save from goalkeeper Aaron Ramsdale.
The visitors rarely tested Martin Dubravka in Newcastle's goal, with David McGoldrick spurning a golden early opportunity when he fired wide after a counter-attack and he hit the crossbar in the second half.
Sheffield United's 29th loss of the season, equalling the record shared by Derby County (2007-08), Sunderland (2005-06) and Ipswich Town (1994-95), consigned them to finishing bottom of the standings with one game left.