The Japanese forward is without a club after leaving Australian side Melbourne Victory in the summer.
Honda, 33, spent 10 seasons in Europe at Dutch club VVV Venlo, CSKA Moscow and AC Milan.
He also comes with international pedigree, having featured for the Japan national team at last years World Cup.
Honda can play anywhere across the front line and on the wing, and offered his services by tagging United in a hopeful message on Twitter – and stating he is happy to play for free.
“Give me an offer,” Honda said. “I don’t need money but I need to play with great team and great team mate.”
United are in the midst of a mini-striker crisis currently, with 17-year-old Mason Greenwood their only fit recognised striker.
Regular front two Marcus Rashford and Anthony Martial are both out injured, while Romelu Lukaku and Alexis Sanchez have joined Inter Milan without being replaced.
Honda scored eight goals for Melbourne last season, and grabbed 10 for Mexican side Pachuca the year before.
Although given his advancing yeras, it is unlikely United will make a move for the veteran, with boss Ole Gunnar Solskjaer placing a firm focus on adding youth to his squad.
One current United player putting himself forward for a more attacking role at Old Trafford though is new summer signing Harry Maguire.
Speaking ahead of the Red Devils’ clash with Arsenal , Maguire said: “I see myself as a threat.
“I’ve had a couple of headers this year up to now and I’m sure to get on the end of many more crosses and create chances in the box. It’s something I take pride in as I work on it on the training pitch.
“I like to say I’ll chip in with some goals to help the team out in terms of getting some good results.”
Suppose you could always get your kit on, Ole.