Canadian midfielder Scott Arfield and goalkeeper Allan McGregor are Gerrard's first two signings for the Scottish giants. The 35-year-old is on a £130,000-a-week contract at Bournemouth so the South Coast club would have to agree to cover the vast majority of his salary.
McGregor has 38 Scotland caps and his form was rewarded with a recall from Alex McLeish recently.
He played all 46 league games as the Tigers finished 18th.
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McGregor started his career at Ibrox and had loan spells with St Johnstone and Dunfermline Athletic before becoming a first-team regular.
The 20-year-old hitman is wanted on a loan to lead the Rangers attack next season and it's claimed that informal talks between himself and Reds' boss Jürgen Klopp have already taken place to establish if a deal could be worked out.
The 38-cap Scotland worldwide won three league titles, a hat-trick of Scottish Cups and five League Cup titles during his first Rangers stint. "We need to win games, it doesn't matter who you're playing, every game is an opportunity for three points. If you keep doing that, that's what wins you titles".
Rangers could be set for an influx of players with huge Premier League experience, if the latest rumours are to be believed. However, he spent a season in Turkey before signing for Hull City in 2013.