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Bournemouth have won one of their last eight league games, a run which has seen them slide from eighth to 14th in the table just six points above the drop zone after 24 games.
"(Manager) Eddie (Howe) runs a tight ship. They will stick together, that's what's made them what they are. They have no big heads," Redknapp, who managed Bournemouth from 1983 to 1992, told the Bournemouth Daily Echo.
"They look like a great bunch of lads, so there's no problem there. They probably need four wins – and perhaps a couple of draws – and they'll be safe. There is enough quality in the team to pick up those results, no doubt."
Redknapp also praised Howe's refusal to sacrifice his footballing principles for a more pragmatic approach as the battle for top-flight survival heats up.
Asked if he believed Howe was right to stick to his attacking approach, Redknapp said: "Absolutely, that's what has made Bournemouth what they are. They play fantastic, open attractive football. They score goals
"They've not come into the league and tried to bore everybody to death by hanging on for results. They've taken it to other teams."
Bournemouth host third-placed Manchester City on Monday.
Kick off is at 22:00.
