Walker is alleged to have spat after a confrontation with supporters outside the players' tunnel at The Dell following the stormy game that Spurs won 1-0. Southampton's chief safety officer, Mike Pallett, said the club had received complaints from a number of fans and these had been passed on to the police.
But in a statement, Walker said: "It's absolute rubbish to say I spat at anyone. I think spitting at people is disgusting and I would never do that.
"It sounds like supporters trying to get me into trouble because their team lost. But I'm quite happy for the FA to investigate these claims because I'm innocent. I have nothing to be ashamed of. My conscience is clear."
Aston Villa's manager, John Gregory, will not be appealing against his latest Football Association misconduct charge for criticising referees after taking advice from the League Managers' Association.
Gregory originally planned to attend a personal hearing on Thursday to plead his case after being charged for comments made to the fourth official during the Premiership clash at Leicester in September.
But the normally outspoken Gregory has changed his mind after talks with the LMA's chief executive, John Barnwell, and will now accept the verdict of the FA disciplinary commission.
Barnwell said: "I am not going to go into private conversations I have had with John Gregory but we have discussed his FA case and he is not going to appeal against it."
Gregory must now wait to see what kind of punishment the FA will decide to take after having already been in the dock this season for comments towards the referee Uriah Rennie at Newcastle in August. On that occasion he received a pounds 2,000 fine and a subsequent appeal by the Villa manager was rejected at a hearing at St Andrews.
Villa's captain, Gareth Southgate, will attend a personal hearing at the same commission to answer a misconduct charge following his comments to the referee when he was sent off in last month's match against Leicester City at Filbert Street.
The German defender Thomas Helmer could be on his way back from Hertha Berlin to Sunderland after being ruled out of action for eight weeks. Helmer was loaned out to the Bundesliga team after failing to settle in the Premiership and the initial deal expires at the end of December.
Now an operation on his damaged Achilles is set to keep him out of action for two months. His tendon injury was sustained during Hertha's final Champions' League group game against Chelsea and it was initially thought that a period of rest would suffice for the 34-year-old to recover.
However, the club's doctor, Hans William Mueller, has since decided that an operation will be necessary to ensure a full recovery.