The US TV talk show host has urged the British soccer star - who already has several inkings on his body - to consider a new etching in tribute to her.
When Ellen made the suggestion, David laughed and replied: "I'm very tempted."
During the interview, David - who got 10 roses tattooed on his arm in July to celebrate his 10-year wedding anniversary with his wife Victoria - revealed the former Spice Girls star loves it when he surprises her with thoughtful gestures.
He said: "I always seem to do pretty well. She always seems to be happy with the gifts that I get her. We always try to do special things for each other.
"It's not always about buying gifts for each other. We just make sure that we spend time together or go for dinner together. That is important to us."
The 34-year-old Los Angeles Galaxy star went on to say he would love to work with Victoria on another underwear campaign for Emporio Armani.
David - who posed with his wife in several steamy shots for the fashion house - said: "We never get a chance to work together and when we do, it's amazing. It was great to work with her on the day."