Phoenix has launched a mandatory bid for Hornby, after offering to buy a stake from another investor that would gave it a 55% holding in the firm.
The offer, of 32.375p per share, values Hornby - which also owns the Scalextric and Airfix brands - at £27.4m.
Hornby has advised investors to take "no action for the time being".
The toymaker also said it had appointed David Adams as its interim chairman, replacing Roger Canham who resigned from Hornby's board on Wednesday. Mr Canham is also the non-executive chairman of Phoenix Asset Management.
On Wednesday, Hornby had reported falling revenues and deepening annual losses.
The company is struggling to revive its fortunes, which has led to it cut back the number of products it sells.
In the year to 31 March, revenues fell to £47.4m from £55.8m, while underlying losses widened to £6.3m from a £5.7m deficit last year.
Model toymaker Hornby has said a takeover offer from its largest shareholder, Phoenix Asset Management, "significantly undervalues" the firm.