The former England Under-21 boss was put in charge for four matches after Sam Allardyce was sacked in September for behaving "inappropriately" when seeking a lucrative sideline role while talking to undercover reporters.
"I think when you are in the position I am in you need to be clear of what is being asked," Southgate told a Football Journalism degree class at the University of Derby.
"There is a big difference, for example, between being asked to take the team over the summer or to take the team for three years or take the team for a year and a half.
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"I don't think it is as easy as saying, 'yes I would like the job'. I would also like to see how it is affecting my family and my health probably," said Southgate.
The former England defender has two more games in charge after having led the side to a 2-0 home win over Malta and a 0-0 draw against Slovenia in World Cup qualifying matches.
Southgate's men host bitter rivals Scotland in a World Cup qualifier on Nov. 11 before entertaining Spain in a friendly four days later.
(Writing by Tony Jimenez; Editing by Andrew Both)
