Warburton is also confident of concluding a deal for a new striker before the end of this week.
Full-back Hodson, who was part of Northern Ireland’s Euro 2016 squad but did not feature, helped Kilmarnock remain in the Premiership last season when on loan from MK Dons and worked with Warburton at both Watford and Brentford.
He will not fly out to South Carolina where Rangers are training this week as he needs more time off. But 34-year-old Onyewu, who played for AC Milan, Standard Liege and Sporting Lisbon, has joined up with the squad in the States and is hoping to clinch a deal.
Warburton said: “Oguchi is someone we have been told about by Niko Kranjcar’s agent. He is coming down to train with us and we will see how he gets on.
“This is the first time I have seen him. He will need the first couple of days to acclimatise in terms of the pace of the session and getting to know the boys.
“We are having a look at him physically in terms of his shape and dealing with the technical level. We will see how he gets on.
“He’s very promising. He’s suffered some injuries in the past and maybe hasn’t realised his potential yet. He’s certainly one to look at now he’s more mature. We will see how he gets on.
“It’s a position we are looking to strengthen. I will look at him for ten days and then say ‘thanks very much’ and see what happens. If he does well then great, fantastic.
“If you have three centre halves then you’re vulnerable to injury or suspension. We need a fourth one definitely.
“We are looking for another two players including another striker.”