Parkinson joined the Reds in 2011 and was responsible for the overall delivery of the customer experience at the club.
Markovic, Wilson and Flanagan have left the club on loan until the end of the season, while Lloyd Jones has left Liverpool on a permanent deal.
Joleon Lescott feels Liverpool could yet make a signing on the final day of the January transfer window.
Manchester United and Manchester City have invested heavily in recruiting new players and are also ready to pay their players big wages.
Shaka Hislop believes Liverpool should target "realistic" AC Milan goalkeeper Gianluigi Donnarumma to solve their issues at the back.
Lazar Markovic is keen to leave Liverpool before the transfer deadline after realising that he has no future under Jurgen Klopp.
Liverpool manager Jurgen Klopp is remaining coy on the future of Emre Can and has also hinted that the club could conduct more transfer business on deadline day.
Liverpool respond to successive defeats and move level on points with third-place Chelsea as goals from Emre Can, Roberto Firmino and Mohamed Salah seal a 3-0 win at Huddersfield.
Christian Purslow believes Liverpool would have received a world-record fee for Philippe Coutinho had they waited until the summer to sell him to Barcelona.
Markovic has not played for Liverpool for over three years and spent the second half of last season on loan at Hull City.
Jurgen Klopp's side were knocked out of the FA Cup by West Bromwich Albion at Anfield over the weekend.
Liverpool have been found culpable of struggling to break down teams who sit back to defend, while easily getting the better of their top six rivals.
Liverpool midfielder Can was reported to have agreed a £85,000-a-week deal with Juventus earlier this month, but Marotta stressed that nothing is done yet.
Julian Brandt is open to extending his Bayer Leverkusen contract despite interest from the likes of Barcelona, Liverpool and Bayern Munich.
Monaco vice-president Vadim Vasilyev has warned Liverpool and Arsenal that Thomas Lemar will not be leaving the French club this month.
Daniel Sturridge was not guaranteed regular playing time in the second-half of the season by Jurgen Klopp.
Newcastle United were told to increase their offer for Feyenoord striker Nicolai Jorgensen before a deadline on Monday evening which has now passed.
Liverpool favourite Mark Lawrenson says Jurgen Klopp may reach out to the club's owners over another January signing.
Newcastle were expecting Sturridge to travel up north on Monday (29 January) but the Baggies have hijacked their move for the 28-year-old.
Liverpool striker Daniel Sturridge is believed to be undergoing a medical at West Brom after the Baggies moved to beat Newcastle and Inter Milan to a £1.5m loan deal.
Jurgen Klopp has ruled out the possibility of Liverpool buying a replacement for Philippe Coutinho before Wednesday's transfer deadline, insisting the club must not panic.
Keita has been rather productive for Monaco since joining from Lazio in the summer, scoring six goals and providing a further five assists in all competitions.