The former England skipper has played only 360 minutes of football since his move to the Los Angeles Galaxy and is set to train with an English club over the winter as he aims to return to full fitness following ankle and knee injuries.
Beckham will now look to train with an English side within easy reach of his Hertfordshire home and Magilton - a former team-mate of Galaxy coach Frank Yallop - will invite the 32-year-old to Portman Road.
Magilton told the Daily Telegraph: "I would love to have David Beckham training with us.
"If it helps him out then he would be very welcome here indeed.
"It would give our players a huge boost to be training with someone of his calibre and give the whole place a huge lift.
"I will invite David to train with us. Ideally I would also love to have him play a couple of games but I doubt that would be possible."