Reports from various sources have Rangers looking to sign a host of big names in the summer transfer window.
The Liverpool legend is keen to bolster his ranks ahead of an assault on the Celtic stronghold in the Scottish Premiership, and is apparently identifying players he played alongside during his career as potential options - with Martin Skrtel being another ex-Red linked with a move to Ibrox.
The goalkeeper won eleven major titles with Rangers including league titles in 2009, 2010 and 2011.
McGregor, who has 38 global caps, moved to Hull after a year in the Turkish top flight.
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The Daily Star have since looked to quash the rumours having claimed that Rangers have denied making a bid for the defender, but there remains an expectation that Gerrard is likely to sign either current or former Liverpool teammates in Glasgow this summer, or pinch a few young up-and-coming players from the academy.
"When the chance came, it was an absolute no-brainer, so I'm buzzing to be back", he told Rangers TV.
The 36-year-old has spent five years at Hull and has played for them in an FA Cup final and in Europe.
"I started training here when I was 12 years old and used to come through the main stand maybe twice a week".
Allen said: "We need people that can handle the pressure, who understand what it means to wear the shirt and cope with playing in it".