The Dude Birds have been linked with both Mahlambi and Tiyani Mabunda from Mamelodi Sundowns, whose large squad could need trimming before the transfer window closes.
However, at this stage Mogashoa does not envision more new faces to join the squad they have assembled for the 2020/21 season.
"We are done signing. We are happy with the squad we have now for this season," Mogashoa tells KickOff.com.
"There has been talk about Mahlambi but that will depend on the terms of the package if we could afford it."
Swallows won their first DStv Premiership match 1-0 when they beat Bloemfontein Celtic 1-0 in Soweto on Wednesday after a 1-1 draw at Stellenbosch FC in their first fixture.
Elasto Kapowezha - Signed as the new Swallows FC team manager
Daniel Gozar - Signed from Free State Stars
Kagiso Malinga - Signed from SuperSport United
Musa Nyatama - Signed from Highlands Park
Ruzaigh Gamildien - Signed from Chippa United
Wandisile Letlabika - Signed from Bloemfontein Celtic
Thabo Mosadi - Signed from Ajax Cape Town
Joseph Mhlongo - Signed after Black Leopards exit
Kamohelo Mahlatsi - Signed from SuperSport United on a five-year contract
Thabo Matlaba - Signed after leaving Black Leopards
Sammy Seabi - Signed on loan from Mamelodi Sundowns
Thela Ngobeni - Signed from Highlands Park
Moeketsi Makhanya - Signed from JDR Stars
Phetso Maphanga - Signed after Chippa United release
Keegan Ritchie - Signed after Bidvest Wits release
Sifiso Hlanti - Signed after Kaizer Chiefs' transfer ban appeal failed
Njabulo Ngcobo - Signed from Uthongathi FC
Junaid Sait - Signed after leaving Cape Umoya United
Kgaogelo Sekgota - Signed after leaving Vitoria Setubal in Portugal