Following the departure of Luis Suarez for a fee that could rise as high as £75million, manager Brendan Rodgers will reportedly be allowed to reinvest the money received from Barcelona.
It is understood that 20-year-old Serbian winger Markovic will command £25million to secure his services from Benfica, while 19-year-old Belgian striker Origi has been in advanced talks regarding a £10million switch to Anfield from Lille.
The Reds have already spent just short of £40million this summer on the signings of Rickie Lambert, Adam Lallana and Emre Can, as Rodgers looks to bolster his squad ahead of their Champions League return this season.
Southampton defender Dejan Lovren and Swansea striker Wilfried Bony have also been heavily linked with moves, and Ayre insists says that further deals are likely to be done as the new campaign nears.
"It's all about building and progress. We’ll aim to continue that throughout the summer," he told the Liverpool Echo.
"We've obviously sold Luis, but we've had a busy few weeks with players arriving as well."
Liverpool's pursuit of Sevilla full-back Alberto Moreno appears to have drawn to an unfruitful close and reports have now suggested that Swansea's Ben Davies could be an alternative option, although Tottenham have also been linked.