The former footballing pro, 46, was photographed on a night out with Bowden in April but is now thought to have parted ways with the 34-year-old in order to focus on his children and his career.
“Jamie enjoys Lizzie’s company, but feels they are too different to pursue anything long-term,” a source told The Sun.
“His priority is his two sons and career, and he wants to hold out on finding the right woman to settle down with. He has a strong group of mates and a healthy social life so he is enjoying spending time with them.”
Standard Online has approached representatives for Redknapp for further comment.
Redknapp split from wife Louise in 2017, with earlier reports suggesting that he had “bided his time” before dating someone new “out of courtesy” to his ex.
The former couple married in 1998 on a luxury yacht and share two sons, Charley, 15, and Beau, 10.
The singer filed for divorce in 2017, stating that their relationship had irretrievably broken down because of the sports pundit’s “unreasonable behaviour.”
Louise, who has recently finished a stint in the West End production of 9 to 5, addressed the split in a recent interview, claiming that her time on Strictly Come Dancing was not to blame for the breakdown of her marriage.
“Strictly put the fire back in my belly, but it didn’t break up my relationship,” she told The Guardian. “After 20 years of marriage, it takes a lot more than that.”
She admitted that she felt “lonely” after putting her music career on hold to focus on her young family.
“It was fine when they were young, because I’d pick them up at 12,” she said. “Then it changed; they’re at school and doing sport, Jamie was doing his thing and there was pure panic. I was lonely and I felt like I had nothing to say.”