Welsh Premier League champions Total Network Solutions (TNS) have put the club's name up for auction online in an attempt to find a new sponsor.
TNS has sponsored the club since 1997
It is understood to be the first time a football club has used the internet to secure this kind of deal.
The club in Llansantffraid, Powys, have been looking for a sponsor since TNS Ltd, the firm behind the club, was bought by British Telecom (BT).
At the time of writing, the highest bid on auction site eBay stood at £12,935.
TNS, called Llansantffraid FC until 1997, have already qualified for next season's UEFA Champions League by winning the Welsh Premier League title.
Since buying the club, Shropshire-based TNS Ltd has steered the team to other Welsh Premier titles, the Welsh Cup and the Champions League.
Last summer, the Saints, as the club is known, played holders Liverpool in a high-profile two-leg Champions League tie.
But TNS's association with the team ended on Wednesday with a 2-0 defeat at Aberystwyth in the final game of the 2005/06 season.
The hunt for a sponsor was sparked by TNS Ltd's acquisition by telecommunications giant BT in a multi-million pound deal in October.
BT pledged to safeguard the 92 jobs at TNS' headquarters in Oswestry, but said it would not be involved with the football club.
Carla Evans, a spokeswoman for the club, said: "We were thinking of the best way to attract a new sponsor and eBay seemed the quickest and easiest way to do it.
"It's a pretty rare opportunity and whoever wins will have the chance to name the team."
The village club's success on the pitch in Wales had only been eclipsed by its award-winning owners in the boardroom.
Mike Harris managing director of the new company, now called BT TNS, said his firm's sponsorship deal with the club had been largely responsible for the rapid growth of TNS Ltd.
Last year, TNS FC said it was planning to move the first team across the border to play at a new 3,000-seater stadium in Oswestry.
But the club plans to continue to run its current ground at Treflan in Llansantffraid for reserve and junior teams.
The online auction closes on 4 May.