The firm said it had received separate proposals from Integrafin Holdings and Epiris LLP in conjunction with its associate James Hay Partnership Management regarding possible cash offers.
The company is also in preliminary talks with Aquiline Capital Partners and Allfunds (UK) regarding potential offers for the business.
Nucleus stressed that discussions between itself and the respective parties were ongoing and there was no certainty that any offer would be made.
Nucleus, which chief executive David Ferguson set up with the backing of a number of financial advice firms in 2006, has developed software platforms that enable financial advisers to provide online access to clients for investments across ISAs, pensions and bond accounts.
The “wrap platform” provider, which floated in 2018, is seen as one of the biggest successes of Scotland’s burgeoning fintech – financial technology – sector.
It said Sanlam UK, which owns just over half of Nucleus’s issued share capital, was supportive of the board engaging in potential offer discussions.
In October, Nucleus said it was continuing to invest in the business as it revealed that assets under administration had risen above £16 billion over the summer.
Gross inflows of £373 million were recorded in the third quarter to the end of September, a slight reduction on the previous quarter (£384m) as a consequence of the pandemic.
Net inflows for the quarter fell by 26.1 per cent, year-on-year, to £82m, but were up by 44.7 per cent in the year-to-date compared to the same period in 2019.
In its trading update, the firm noted that advisers actively using its platform remained broadly flat against the comparable period. Customer numbers were up 4.1 per cent year-on-year.
Despite the ongoing impact of the pandemic on investor sentiment and market growth, assets under administration (AUA) stood at £16.1bn at September 30, up 1.8 per cent on the previous quarter and 2.6 per cent year-on-year.
By comparison, the FTSE All-Share Index fell 3.8 per cent on the last quarter and was down 19.2 per cent year-on-year.
Ferguson said at the time: “Covid-19 looks set to dominate our lives for at least the remainder of the year and is likely to have a continued impact for a time to come.
“In these challenging times, the health and well-being of our staff remain our highest priority. While we have re-opened a portion of the office, within government guidelines, almost all of our people continue to work from home.
“Despite a significant reduction in markets this year… our AUA at the end of Q3 2020 was back to the level we started the year, at £16.1bn.
“Despite a softer Q3 in terms of net inflows, our year-to-date position remains ahead at £515m compared to £356m in 2019, a 44.7 per cent increase on the same period last year. It’s worth noting that in terms of gross inflows, while these dipped in August the figures for September are more positive.”
Shares were up 32 per cent shortly after news of the possible takeover offers.