Redknapp is currently looking to add experienced players to his squad ahead of Tottenham's debut Champions League campaign, but West Ham reacted angrily to their attempts to sign club captain Parker.
However, reports suggest Parker, 29, may be keen on the move as he wants Champions League football and Redknapp feels Spurs did nothing wrong.
"Any club is perfectly entitled to make an enquiry about a player from another club," he said. "West Ham have been interested in Jamie O'Hara for some time and I don't have a problem with that.
"We get people ringing us up all the time asking about our players' availability - it's how the whole business works. This club has behaved correctly.
"We didn't go public on our interest in Scott - we approached West Ham through the proper channels. If our chairman wants to improve the offer that's up to him, but I like Scott, he's a good player."
He added: "I'm sure the chairman must have got some encouragement or he wouldn't have made an offer, so I'm not sure the full story has been told about that one.
"The chairman wouldn't have made an offer unless he thought there was a chance that they wanted to do something."
Redknapp has also long been linked with a move for Manchester City forward Craig Bellamy.
Roberto Mancini said this week he was unsure whether Bellamy, 31, would make his 25-man squad for the new season and, while Redknapp had previously told Soccernet the player's wages may prove prohibitive, the Spurs boss has now suggested he would be interested.
"I like Craig Bellamy but I don't know if they would sell him," said Redknapp. "The chairman deals with all the transfers. He asks me what I want and I tell him. I don't know where he's at with Bellamy, if anywhere."
Speaking after Spurs lost 4-1 to Villarreal in a friendly at White Hart Lane on Thursday, Redknapp said he felt his squad was lacking experience.
"If you're going to be really successful you need a few men in your team, not lads that are learning," he said. "We've got a good group of players but two or three players with experience would make a massive difference to the team.
"You look at Inter Milan - they won the Champions League with a team of men, they were all experienced players. You need players with experience."