Marcel Brands left the club in December and has yet to be replaced.
Lampard is in his third week at the club after replacing Rafael Benitez at the end of last month, while Everton have been without a director of football since the departure of Marcel Brands in December.
“We’ll see going forward,” said Lampard, whose side play at Southampton on Saturday. “I will have an opinion on it. I think working with a director of football, of course many clubs do.
“The key for me is the communication and the fact everything is aligned and you’re working in the same direction. If you can get that mix, great. That can be a really positive force for the club.”
Lampard said Everton had yet to complete a strategic review “across the board” following Brands’ departure.
“My feeling is of course I would like an input into that, I think it’s my role to, to a degree,” the former Derby and Chelsea manager said.
“But my first role at this club is to get us winning football games and the amount that that consumes you, it’s been so important in these first two or three weeks to put my head completely into that, working with the squad.
“So that’s where we’re at in this process and the club will make their decisions on that. When asked for my input I’ll most certainly give it.”
Everton secured their first Premier League win under Lampard in last Saturday’s 3-0 victory against Leeds, which eased their relegation fears having won only one of their previous 15.
Lampard said: “It’s been good for the confidence of the group, coming in here with quite a long, difficult run of results, so clearly that is the first thing, it can give you a bounce.
“But we have to keep ourselves very settled and understand that it’s one result – we’ve had two wins, one in the (FA) Cup, one in the league.
That record away from home is a difficult one to look at and we need to try and change it
“There’s a lot of work to be done, but it was a nice template to move forward from.”
The Merseysiders’ solitary away win in the league this season came at Brighton in August and they face a tough test at in-form Southampton if they are to improve their poor record on the road.
Lampard added: “My job is to not be overly excited and look at what’s next in front of us. It’s an away game, different challenges, different team.
“That record away from home is a difficult one to look at and we need to try and change it.”
Lampard, who has no new injury worries, will be boosted by the return to contention of Ukraine defender Vitalii Mykolenko.
Winger Demarai Gray (hip) and midfielder Abdoulaye Doucoure (groin) are hoping to be back next week, while Yerry Mina (thigh), Fabian Delph and Ben Godfrey are still out.