And the Blues boss is weighing up a summer return for the former Cetlic youngster, with a sizeable overhaul of his squad in the offing.
Lindsay’s existing deal comes to a close at the end of the season, but Rotherham have an option in their favour to extend that agreement.
Paul Warne’s side are going for promotion, although they are struggling at present with one league win in six.
The Rotherham boss explained much will depend on where his side are playing next season, but he’d like to see the 26-year-old stay at the New York Stadium.
Warne told the Rotherham Advertiser: ‘We’ll see what league we’re in in the summer.
‘If Jamie would like to sign a deal then that would be great.
‘I’d like to think he sees his future with us.
‘I have spoken to him and told him I’d love him to stay for longer.’
Even if Lindsay looks to move on from Rotherham, it’s expected his club will take up the option to extend his deal in an effort to protect their asset.
That would mean Pompey having to shell out a fee to bring the midfielder to Fratton Park.
Warne added: ‘If Jamie has no intention of staying then, like all our players, he has a value to the club and we will try to get that value back.’