Oxford United striker James Constable is not looking to leave the club, and will not join another League Two side, BBC Radio Oxford understands.
BBC Wiltshire reported that Swindon Town made a second bid for the 27-year-old on Thursday, having had an initial offer rejected this week.
Constable himself also said on social networking site Twitter he had not asked to join Oxford's arch-rivals.
"I have never asked to speak to Swindon," said Constable.
He also retweeted BBC Radio Oxford's post: "We hear from a trusted source that James Constable is not looking for a move from Oxford United and certainly not to another League Two club."
Constable has been a key player for the U's this season, playing 27 games and scoring nine times and helped fire them up to seventh in the League Two table.
"Yes there has been a formal bid and we have turned it down. I'm not surprised by it," Wilder told BBC Radio Oxford on Thursday.
"We've got a lot of good players at this club and James is one of those.
"Until the situation progresses he is with us and his attitude has been first class when there has been talk and speculation in the past and I expect that to be the same now."
Constable began his career at Walsall and played for Kidderminster and Shrewsbury before joining the U's permanently in July 2009.
Wilder added: "I've spoken to 'Beano' and told him to get his head down and get on with doing well for the football club.
"We're it a good situation in the league and we need to focus on a big game versus Crewe on Saturday."