The investigation comes after a member of the public complained to police about racist and homophobic abuse following Sunday's match against Spurs at Fratton Park.
A large number of Spurs fans hurled vile abuse at the Pompey skipper – a former Spu
rs player who upset fans by moving to arch-rivals Arsenal in 2001.
Although police were at the match, no arrests were made and there were initially no plans to launch a criminal investigation.
They only acted after the complaint was made.
Officers would not discuss the case, claiming that they did not want to prejudice a separate investigation being undertaken by the Football Association. The force has made a formal complaint to the FA about the abuse.
The FA said its own investigations were in the very early stages.
FA equality manager Lucy Faulkner said: 'In principle what we have is the ability to charge clubs for failure to control fans.
'We will work with Hampshire Constabulary to gather the evidence before we know what to do next.'
Spurs indicated that the club would attempt to involve Pompey in the investigation.
A spokesman said: 'We do not tolerate racist, homophobic or obscene chanting at White Hart Lane and we have clamped down on it. We are now waiting for a full report from Portsmouth to hear how this matter was dealt with at Fratton Park.'
Pompey spokesman Gary Double, pictured below, said: 'We are very happy that the FA and police are working together to tackle a situation that needs to be resolved.
'From our perspective we are going to concentrate on the UEFA Cup game tonight then we are going to sit down with Sol and work out what he wants to do about it.'
The club has said that it will not make a complaint, although it would support Campbell if he decided to.
Some Pompey fans were angry that arrests were not made on Sunday.
Tony Goodall, from the Portsmouth Independent Supporters' Asso-ciation, said: 'It's the second season now Spurs have come down and abused Sol.
'I know the police said there were too many fans involved but it has to start with someone and they should make examples of them.
'Plus, why didn't Pompey tell Spurs fans to stop over the loudspeakers?'
Harry Redknapp said: 'It's got no place in football what went on Sunday, it's got no place in life in my opinion, it was a disgrace.
'I would like something done about it.'
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