In a statement issued on Thursday, Ms Little-Pengelly added that she had been “deeply saddened” by what has happened in the party over the last number of weeks.
Ms Little-Pengelly is a former South Belfast MP but she lost her seat to the SDLP’s Claire Hanna in 2019. She later became Mrs Foster’s special adviser.
Mr Poots and Mrs Foster are both set to attend a British Irish Council meeting on Co Fermanagh on Friday.
Mr Poots said he is happy to meet with Mrs Foster at any time.
Tom Topping: Funeral details released after shock death of popular businessman - daughter tells of how her world is ‘totally shattered’
Michelle O’Neill has kicked sand in the face of victims of terrorism
‘Warped revisionism’ claim after Sinn Fein praise for hunger striker
Major Belfast route remains closed after gas leak
PSNI appeal for information after 50 firefighters fight 'suspected arson' attack at former entertainment centre - 'fire started after access was gained to the building via a vent on the lower ground floor'
The pair are not believed to have met since she was ousted from the leadership of the party last month.
“I am happy to meet Arlene any time and if Arlene wants to meet me, I’ll be very happy to have those conversations with her,” he said.
“I wish her well, I wish her family well, and I want us all to move on and move forwards, and keeping that relationship open is something I would desire.”
Mrs Foster earlier attended her final Executive meeting as First Minister.
It was put to Mr Poots that he stayed silent at the end of the meeting as other ministers wished her and the other departing DUP ministers Diane Dodds, Peter Weir and Gordon Lyons well.
He responded: “I will be making my position clear on Monday on that, there’s the opportunity for a statement to be made in the House and I would hoping to participating there.”