In 2007, Gallas was named Arsenal's captain, but lost the role during the 2008-09 season after criticising team-mates in an interview.
Related ArticlesVan der Vaart and Gallas to debutDefoe out for three monthsParker never tempted to join SpursVan der Vaart happy to earn SpursJermain Defoe out for six weeksRedknapp 'wouldn't say no' to England jobHarry Redknapp, the Tottenham manager, has not disguised his admiration for the Frenchman, who rejected a new contract at Arsenal in the summer to become a free agent.
'He could easily become a mainstay,' Redknapp said. 'People will say he played for Arsenal but you have to be strong as a person to do that [move from Arsenal to Spurs].
"He could have gone and played somewhere else, but it says so much about the boy that he is willing to put himself on the line. Arsenal and Chelsea were part of his past. You move forward.'
Asked how much a player of Gallas's pedigree would have cost on the open market, Redknapp replied: '£8million or £10million, if you want a player who is a top centre-half to play in the Premier League.
"You have to pay that money, surely. I think he will be a great signing for us. He cost nothing and is not on silly money.'
Redknapp must hope Gallas, 31, has learned from his Arsenal experience.
He lost the Arsenal armband in November 2008 after an interview in which he accused the club's youngsters of lacking the stomach to fight for the Premier League title, claimed he had to separate arguing team-mates during half-time of a 4-4 draw against Tottenham and insisted an unnamed Arsenal player insulted him and several colleagues.
Redknapp will make a late decision on whether to risk King or save him for the game in Bremen on Tuesday. King's recurring knee injury means he will be unable to play both.
'It is a difficult one,' Redknapp said. 'If I play him Saturday I probably won't play him Tuesday. Both competitions are important to me, but we might just need Ledley's experience in an away game in Germany.
"If he plays Tuesday he has an extra day and I might get him the following Saturday. It is a juggling act.'
While Redknapp was considering the captaincy he received more bad news concerning injuries when it was confirmed that Jermain Defoe, expected to be missing for six weeks, had been ruled out for three months.
Tottenham's fears over the injury the striker suffered during England's European Championship qualifier in Switzerland on Tuesday were confirmed following consultation with a specialist.
Now Defoe, who scored a hat-trick against Bulgaria last week, could miss all of his club's Champions League group matches, as well as two England internationals.
A statement on Spurs' official website read: 'Following a review by an ankle specialist, Jermain Defoe underwent surgery to repair torn ligaments in his right ankle.
'The striker was forced off with the injury during England's European Championship qualifier in Switzerland on Tuesday and has been ruled out of action for around three months.'
Defoe was confident after Tuesday night's game that the injury which forced him to be carried off on a stretcher was not serious and that he could even be fit for the weekend.
But he was on crutches at Spurs' training ground on Thursday with a protective boot on his right ankle and the problem is more serious than the injury suffered by Dawson during England's win over Bulgaria seven days ago.
Redknapp will be deeply unhappy that two players so important to Spurs have been injured playing for their country and their absences will seriously test the strength of his squad, bolstered by four summer signings.
At least Luka Modric should be available to return after a hamstring strain, but Jonathan Woodgate's playing career is in doubt while goalkeeper Heurelho Gomes is still missing.
Meanwhile, Liverpool manager Roy Hodgson has claimed that he rejected the chance to scupper Tottenham's deadline day move for Rafael van der Vaart. Van der Vaart completed an £8m transfer from Real Madrid to Spurs last month, but Hodgson insists he turned down the opportunity to sign the Holland midfielder.
Hodgson said: 'I apologise to Rafael van der Vaart if his agent gave him another story because I think he's a very good player, but he's not the profile of the player we were looking for.
'When it came up I said, 'No, we have players in his position.' An agent rings you up to ask if you want to sign Van der Vaart, you say 'No' and then the next minute you're one of the clubs that want to sign him."